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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b4">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span>  st <font color="Olive" title="b1">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Olive" title="b1">f</font> is  <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>) &amp; <font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q</font> &amp;  not <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Olive" title="b1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> holds <br/> for <font color="Olive" title="b5">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b5">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> ex <font color="Olive" title="b6">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b6">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Olive" title="b1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b6">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>) &amp; <font color="Olive" title="b6">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Olive" title="b4">u</font>,<font color="Olive" title="b5">s</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b3">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span>  st <font color="Maroon" title="c2">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>) &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">q</font> &amp;  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> holds <br/> for <font color="Olive" title="b4">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b4">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> ex <font color="Olive" title="b5">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b5">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b5">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>) &amp; <font color="Olive" title="b5">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">s</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span>  st <font color="Maroon" title="c2">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font> &amp;  not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> holds <br/> for <font color="Olive" title="b2">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b2">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> ex <font color="Olive" title="b3">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b3">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b3">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b3">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">s</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">u</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font> &amp;  not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> implies  for <font color="Olive" title="b1">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> ex <font color="Olive" title="b2">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Olive" title="b1">s</font>) ) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:49"/><span class="lab"><font color="Green" title="E31">A1</font></span>: 
( <font color="Maroon" title="c2">f</font> is  <a href="topreal1.html#V1" title="TOPREAL1:attr.1">special</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="sppol_1.html#V3" title="SPPOL_1:attr.3">alternating</a>  )
 <span class="kw">and </span><br/><a NAME="E2:49"/><span class="lab"><font color="Green" title="E32">A2</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">and </span><br/><a NAME="E3:49"/><span class="lab"><font color="Green" title="E33">A3</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">and </span><br/><a NAME="E4:49"/><span class="lab"><font color="Green" title="E34">A4</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:49"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>)
 <span class="kw">and </span><br/><a NAME="E6:49"/><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font>
 <span class="kw">and </span><br/><a NAME="E7:49"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
 not <font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/> ex <font color="Olive" title="b2">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b2">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Olive" title="b1">s</font>) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">p0</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E8:49"/>
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/>
<a NAME="E9:49"/><span class="kw">then </span>
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E10:49"/><span class="kw">then </span>
 <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c1">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="ref" href="topreal1.html#D3" title="TOPREAL1:def.3">TOPREAL1:def 3</a></span>;<br/>
<a NAME="E11:49"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A8</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rltopsp1.html#T68" title="RLTOPSP1:th.68">RLTOPSP1:68</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">s</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) ) )</span><br/>

<span class="kw">assume </span><a NAME="E12:49"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
<font color="Maroon" title="c7">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1"/>
( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font> or <font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) )</span><br/><div class="add"><a NAME="E2:49_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:49"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="rltopsp1.html#T70" title="RLTOPSP1:th.70">RLTOPSP1:70</a></span>;<br/><a NAME="E3:49_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:49"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:49_1_1"/>
 ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2"/><span class="lab"><font color="Green" title="E40">A10</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) )</span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c8">v2</font> = <font color="Maroon" title="c4">q</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">v1</font> = <font color="Maroon" title="c3">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E4:49_1_2"/><span class="lab"><font color="Green" title="E41">A11</font></span>: 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="euclid.html#T17" title="EUCLID:th.17">EUCLID:17</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">r0</font> = <font color="Maroon" title="c7">s</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2 as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/><span class="kw">consider </span><font color="Maroon" title="c11">s0</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E7:49_1_2"/><span class="lab"><font color="Green" title="E42">A12</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:49_1_2"/><span class="lab"><font color="Green" title="E43">A13</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font>
 <span class="kw">and </span><br/><a NAME="E9:49_1_2"/><span class="lab"><font color="Green" title="E44">A14</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:49"><span class="lab"><font color="Green" title="E35">A5</font></span></a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">r3</font> =  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1);<br/><span class="kw">set </span><font color="Maroon" title="c13">r4</font> =  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>);<br/><span class="kw">set </span><font color="Maroon" title="c14">p4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">p3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>;<br/><a NAME="E10:49_1_2"/><span class="lab"><font color="Green" title="E45">A15</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xreal_1.html#T139" title="XREAL_1:th.139">XREAL_1:139</a></span>;<br/><a NAME="E11:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A16</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:49_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a>, <a class="ref" href="xreal_1.html#T139" title="XREAL_1:th.139">XREAL_1:139</a></span>;<br/><a NAME="E12:49_1_2"/><span class="lab"><font color="Green" title="E47">A17</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:49_1_2"><span class="lab"><font color="Green" title="E45">A15</font></span></a>, <a class="txt" href="#E4:49_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="xreal_1.html#T139" title="XREAL_1:th.139">XREAL_1:139</a></span>;<br/><a NAME="E13:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A18</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/><a NAME="E14:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A19</font></span>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T187" title="XCMPLX_1:th.187">XCMPLX_1:187</a></span>;<br/><a NAME="E15:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A20</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><a NAME="E16:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A21</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:49_1_2"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E17:49_1_2"/><span class="kw">then </span>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) &amp;  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T28" title="XXREAL_0:th.28">XXREAL_0:28</a>, <a class="ref" href="xxreal_0.html#T30" title="XXREAL_0:th.30">XXREAL_0:30</a></span>;<br/><a NAME="E18:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A22</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>)
 ;<br/><a NAME="E19:49_1_2"/><span class="lab"><font color="Green" title="E53">A23</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:49_1_2"><span class="lab"><font color="Green" title="E45">A15</font></span></a>, <a class="txt" href="#E4:49_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a>, <a class="ref" href="xreal_1.html#T139" title="XREAL_1:th.139">XREAL_1:139</a></span>;<br/><a NAME="E20:49_1_2"/>
 not  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:49_1_2_1"/><span class="lab"><font color="Green" title="E54">A24</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:49_1_2_1_1"/>
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E14:49_1_2"><span class="lab"><font color="Green" title="E49">A19</font></span></a>, <a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/>
<a NAME="E2:49_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A25</font></span>: 
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49_1_2"><span class="lab"><font color="Green" title="E47">A17</font></span></a>, <a class="txt" href="#E8:49_1_2"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T29" title="XXREAL_0:th.29">XXREAL_0:29</a></span>;<br/>
<a NAME="E3:49_1_2_1_1"/><span class="lab"><font color="Green" title="E56">A26</font></span>: 
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:49_1_2"><span class="lab"><font color="Green" title="E51">A21</font></span></a>, <a class="ref" href="xxreal_0.html#T28" title="XXREAL_0:th.28">XXREAL_0:28</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_1_1_1"/>
(  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 or  <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1_1"><span class="lab"><font color="Green" title="E56">A26</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_1_1_1"/>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>)</span><br/><div class="add"><a NAME="E2:49_1_2_1_1_1_1"/><span class="kw">then </span>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_1_2_1_1"><span class="lab"><font color="Green" title="E55">A25</font></span></a>, <a class="ref" href="xxreal_0.html#T21" title="XXREAL_0:th.21">XXREAL_0:21</a></span>;<br/><a NAME="E3:49_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A27</font></span>: 
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T50" title="XREAL_1:th.50">XREAL_1:50</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c16">r5</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span>;<br/><a NAME="E4:49_1_2_1_1_1_1"/>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c11">s0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:49_1_2"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="txt" href="#E11:49_1_2"><span class="lab"><font color="Green" title="E46">A16</font></span></a>, <a class="ref" href="xxreal_0.html#T20" title="XXREAL_0:th.20">XXREAL_0:20</a></span>;<br/><a NAME="E5:49_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A28</font></span>: 
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T48" title="XREAL_1:th.48">XREAL_1:48</a></span>;<br/><a NAME="E6:49_1_2_1_1_1_1"/>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:49_1_2"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="txt" href="#E15:49_1_2"><span class="lab"><font color="Green" title="E50">A20</font></span></a>, <a class="ref" href="xxreal_0.html#T28" title="XXREAL_0:th.28">XXREAL_0:28</a></span>;<br/><a NAME="E7:49_1_2_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></span>;<br/><a NAME="E8:49_1_2_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A27</font></span></a>, <a class="ref" href="xreal_1.html#T72" title="XREAL_1:th.72">XREAL_1:72</a></span>;<br/><a NAME="E9:49_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A29</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A27</font></span></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></span>;<br/><span class="lab"><font color="Green" title="E60">A30</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A27</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>
<br/>.= 
<font color="Maroon" title="c11">s0</font>

;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T32" title="EUCLID:th.32">EUCLID:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a 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title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T32" title="EUCLID:th.32">EUCLID:32</a></span>
<br/>.= 
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title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span 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class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span 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href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font 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title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> = 
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color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> 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title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a 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class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a 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title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a 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<span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T30" title="EUCLID:th.30">EUCLID:30</a></span>
;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span 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href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T30" title="EUCLID:th.30">EUCLID:30</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 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title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 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title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T30" title="EUCLID:th.30">EUCLID:30</a></span>
;<br/><a NAME="E14:49_1_2_1_1_1_1"/><span class="kw">then </span>
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href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" 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class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T30" title="EUCLID:th.30">EUCLID:30</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span 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title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="txt" href="#E10:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E60">A30</font></span></a>, <a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
;<br/><span class="kw">hence </span><a NAME="E16:49_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A27</font></span></a>, <a class="txt" href="#E5:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E58">A28</font></span></a>, <a class="txt" href="#E9:49_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E59">A29</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_1_1_2"/>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>)</span><br/><div class="add"><a NAME="E2:49_1_2_1_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T16" title="XXREAL_0:th.16">XXREAL_0:16</a></span>;<br/><a NAME="E3:49_1_2_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:49_1_2"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">hence </span><a NAME="E4:49_1_2_1_1_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:49_1_2"><span class="lab"><font color="Green" title="E48">A18</font></span></a>, <a class="ref" href="xcmplx_1.html#T187" title="XCMPLX_1:th.187">XCMPLX_1:187</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E2:49_1_2_1"/><span class="lab"><font color="Green" title="E55">A31</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="sppol_1.html#R1" title="SPPOL_1:pred.1">is_extremal_in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49"><span class="lab"><font color="Green" title="E31">A1</font></span></a>, <a class="txt" href="#E2:49"><span class="lab"><font color="Green" title="E32">A2</font></span></a>, <a class="txt" href="#E3:49"><span class="lab"><font color="Green" title="E33">A3</font></span></a>, <a class="ref" href="sppol_1.html#T36" target="_self" title="SPPOL_1:th.36">Th59</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:49_1_2_1"/><span class="lab"><font color="Green" title="E56">A32</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_1_2"/>
( <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> or <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_1"><span class="lab"><font color="Green" title="E56">A32</font></span></a>, <a class="txt" href="#E1:49_1_2_1"><span class="lab"><font color="Green" title="E54">A24</font></span></a>, <a class="txt" href="#E2:49_1_2_1"><span class="lab"><font color="Green" title="E55">A31</font></span></a>, <a class="ref" href="sppol_1.html#D1" target="_self" title="SPPOL_1:def.1">Def1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_1"/><span class="lab"><font color="Green" title="E57">A33</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_1_2_1_1_1"/>
( <font color="Maroon" title="c11">s0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c11">s0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_1_1_1_1"/>
<font color="Maroon" title="c11">s0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="ref" href="euclid.html#T29" title="EUCLID:th.29">EUCLID:29</a></span>
<br/>.= 
1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T27" title="EUCLID:th.27">EUCLID:27</a></span>
<br/>.= 
<font color="Maroon" title="c4">q</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T29" title="EUCLID:th.29">EUCLID:29</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:49_1_2_1_2_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:49"><span class="lab"><font color="Green" title="E36">A6</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_1_1_1_2"/><span class="lab"><font color="Green" title="E58">A34</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="txt" href="#E1:49_1_2_1_2_1"><span class="lab"><font color="Green" title="E57">A33</font></span></a>, <a class="ref" href="euclid.html#T42" title="EUCLID:th.42">EUCLID:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T38" title="EUCLID:th.38">EUCLID:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span>

;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T37" title="EUCLID:th.37">EUCLID:37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T35" title="EUCLID:th.35">EUCLID:35</a></span>
;<br/><a NAME="E4:49_1_2_1_2_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A35</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="euclid.html#T34" title="EUCLID:th.34">EUCLID:34</a></span>;<br/><a NAME="E5:49_1_2_1_2_1_1_1_2"/>
1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c11">s0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:49_1_2"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="txt" href="#E1:49_1_2_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E58">A34</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:49_1_2_1_2_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:49_1_2"><span class="lab"><font color="Green" title="E53">A23</font></span></a>, <a class="txt" href="#E4:49_1_2_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E59">A35</font></span></a>, <a class="ref" href="xxreal_0.html#T21" title="XXREAL_0:th.21">XXREAL_0:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:49_1_2_1_2_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_2"/><span class="lab"><font color="Green" title="E57">A36</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_1_2_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_1_2_2_1_1"/>
( <font color="Maroon" title="c11">s0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c11">s0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_2_1_1_1"/>
<font color="Maroon" title="c11">s0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="ref" href="euclid.html#T29" title="EUCLID:th.29">EUCLID:29</a></span>
<br/>.= 
1 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T27" title="EUCLID:th.27">EUCLID:27</a></span>
<br/>.= 
<font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T29" title="EUCLID:th.29">EUCLID:29</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:49_1_2_1_2_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49"><span class="lab"><font color="Green" title="E37">A7</font></span></a>, <a class="txt" href="#E11:49"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_1_2_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_1_2_2_1_1_2"/><span class="lab"><font color="Green" title="E58">A37</font></span>: 
<font color="Maroon" title="c11">s0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="txt" href="#E1:49_1_2_1_2_2"><span class="lab"><font color="Green" title="E57">A36</font></span></a>, <a class="ref" href="euclid.html#T42" title="EUCLID:th.42">EUCLID:42</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T38" title="EUCLID:th.38">EUCLID:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span>

;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T37" title="EUCLID:th.37">EUCLID:37</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T35" title="EUCLID:th.35">EUCLID:35</a></span>
;<br/><a NAME="E4:49_1_2_1_2_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="euclid.html#T34" title="EUCLID:th.34">EUCLID:34</a></span>;<br/><span class="kw">hence </span><a NAME="E5:49_1_2_1_2_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:49_1_2"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="txt" href="#E15:49_1_2"><span class="lab"><font color="Green" title="E50">A20</font></span></a>, <a class="txt" href="#E1:49_1_2_1_2_2_1_1_2"><span class="lab"><font color="Green" title="E58">A37</font></span></a>, <a class="ref" href="xxreal_0.html#T29" title="XXREAL_0:th.29">XXREAL_0:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:49_1_2_1_2_2"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div><a NAME="E21:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A38</font></span>: 
 ex <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>) &amp;  not <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">u4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E23:49_1_2"/><span class="lab"><font color="Green" title="E55">A39</font></span>: 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="euclid.html#T17" title="EUCLID:th.17">EUCLID:17</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">u3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E25:49_1_2"/><span class="lab"><font color="Green" title="E56">A40</font></span>: 
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T22" title="XXREAL_0:th.22">XXREAL_0:22</a></span>;<br/><a NAME="E26:49_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E8:49_1_2"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T20" title="XXREAL_0:th.20">XXREAL_0:20</a></span>;<br/><a NAME="E27:49_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:49_1_2"><span class="lab"><font color="Green" title="E56">A40</font></span></a></span>;<br/><a NAME="E28:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A41</font></span>: 
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:49_1_2"><span class="lab"><font color="Green" title="E52">A22</font></span></a>, <a class="ref" href="topreal1.html#T6" title="TOPREAL1:th.6">TOPREAL1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">u0</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E30:49_1_2"/><span class="lab"><font color="Green" title="E58">A42</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T69" title="EUCLID:th.69">EUCLID:69</a></span>;<br/><span class="lab"><font color="Green" title="E59">A43</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="ref" href="euclid.html#T38" title="EUCLID:th.38">EUCLID:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T49" title="EUCLID:th.49">EUCLID:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_3"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_3_1"/>
( <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  not <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_3_1_1"/>
<font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font></span><br/><div class="add"><a NAME="E2:49_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A44</font></span>: 
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#D10" title="XXREAL_0:def.10">XXREAL_0:def 10</a></span>;<br/><a NAME="E3:49_1_2_3_1_1"/>
 <a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></span>;<br/><a NAME="E4:49_1_2_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><a NAME="E5:49_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A45</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T24" title="XREAL_1:th.24">XREAL_1:24</a></span>;<br/><a NAME="E6:49_1_2_3_1_1"/>
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">r0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>
 ;<br/><a NAME="E7:49_1_2_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A46</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">v3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>, <font color="Maroon" title="c20">v4</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><span class="lab"><font color="Green" title="E63">A47</font></span>:  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T187" title="XCMPLX_1:th.187">XCMPLX_1:187</a></span>
<br/>.= 
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>

;<br/><span class="lab"><font color="Green" title="E64">A48</font></span>:  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) = 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">v3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c20">v4</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T5" target="_self" title="SPPOL_1:th.5">Th20</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T69" title="EUCLID:th.69">EUCLID:69</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:49_1_2"><span class="lab"><font color="Green" title="E59">A43</font></span></a>, <a class="ref" href="euclid.html#T11" title="EUCLID:th.11">EUCLID:11</a></span>
;<br/> <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T52" title="COMPLEX1:th.52">COMPLEX1:52</a></span>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:49_1_2"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="txt" href="#E2:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
;<br/><a NAME="E12:49_1_2_3_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="txt" href="#E5:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E61">A45</font></span></a>, <a class="txt" href="#E9:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E63">A47</font></span></a>, <a class="ref" href="xreal_1.html#T64" title="XREAL_1:th.64">XREAL_1:64</a></span>;<br/><a NAME="E13:49_1_2_3_1_1"/><span class="kw">then </span>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">r0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:49_1_2"><span class="lab"><font color="Green" title="E55">A39</font></span></a>, <a class="txt" href="#E10:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E64">A48</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>;<br/><span class="kw">hence </span><a NAME="E14:49_1_2_3_1_1"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2_3_1_1"><span class="lab"><font color="Green" title="E62">A46</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_3_1_2"/>
 not <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A49</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:49_1_2"><span class="lab"><font color="Green" title="E59">A43</font></span></a>, <a class="ref" href="xxreal_0.html#D10" title="XXREAL_0:def.10">XXREAL_0:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">v3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>, <font color="Maroon" title="c20">v4</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E4:49_1_2_3_1_2"/><span class="lab"><font color="Green" title="E61">A50</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">r0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>
 ;<br/> <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) = 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">v3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c20">v4</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T5" target="_self" title="SPPOL_1:th.5">Th20</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T69" title="EUCLID:th.69">EUCLID:69</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_1_2_3_1_2"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="ref" href="euclid.html#T11" title="EUCLID:th.11">EUCLID:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T67" title="COMPLEX1:th.67">COMPLEX1:67</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:49_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c10">r0</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T52" title="COMPLEX1:th.52">COMPLEX1:52</a></span>
<br/>.= 
<font color="Maroon" title="c10">r0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:49_1_2_3_1_2"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c16">u4</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E4:49_1_2_3_1_2"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E33:49_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">u4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u7</font> where <font color="Olive" title="b1">u7</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> :  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c18">u0</font>,<font color="Olive" title="b1">u7</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font> </span> } </span> 
 ;<br/><a NAME="E34:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A51</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c18">u0</font>,<font color="Maroon" title="c7">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T17" title="METRIC_1:th.17">METRIC_1:17</a></span>;<br/><span class="lab"><font color="Green" title="E61">A52</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:49_1_2"><span class="lab"><font color="Green" title="E42">A12</font></span></a>, <a class="ref" href="euclid.html#T38" title="EUCLID:th.38">EUCLID:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T26" title="EUCLID:th.26">EUCLID:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T33" title="EUCLID:th.33">EUCLID:33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T40" title="EUCLID:th.40">EUCLID:40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T49" title="EUCLID:th.49">EUCLID:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2_5"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_5_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:49_1_2_5_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> or  not 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_5_1_1"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_5_1_1"/><span class="lab"><font color="Green" title="E62">A53</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font></span><br/><div class="add"><a NAME="E2:49_1_2_5_1_1"/>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T17" title="XXREAL_0:th.17">XXREAL_0:17</a></span>;<br/><a NAME="E3:49_1_2_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A54</font></span>: 
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c11">s0</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><a NAME="E4:49_1_2_5_1_1"/>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2_5_1_1"><span class="lab"><font color="Green" title="E62">A53</font></span></a>, <a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">XXREAL_0:def 9</a></span>;<br/><a NAME="E5:49_1_2_5_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:49_1_2"><span class="lab"><font color="Green" title="E44">A14</font></span></a>, <a class="ref" href="xreal_1.html#T48" title="XREAL_1:th.48">XREAL_1:48</a></span>;<br/><a NAME="E6:49_1_2_5_1_1"/><span class="kw">then </span>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_2_5_1_1"><span class="lab"><font color="Green" title="E63">A54</font></span></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>;<br/><a NAME="E7:49_1_2_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A55</font></span>: 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T64" title="XREAL_1:th.64">XREAL_1:64</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">v3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>, <font color="Maroon" title="c20">v4</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E9:49_1_2_5_1_1"/>
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">r0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>
 ;<br/><a NAME="E10:49_1_2_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A56</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>;<br/> <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) = 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">v3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c20">v4</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T5" target="_self" title="SPPOL_1:th.5">Th20</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T69" title="EUCLID:th.69">EUCLID:69</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:49_1_2"><span class="lab"><font color="Green" title="E61">A52</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T11" title="EUCLID:th.11">EUCLID:11</a></span>
;<br/><a NAME="E12:49_1_2_5_1_1"/><span class="kw">then </span>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">r0</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:49_1_2"><span class="lab"><font color="Green" title="E55">A39</font></span></a>, <a class="txt" href="#E7:49_1_2_5_1_1"><span class="lab"><font color="Green" title="E64">A55</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>;<br/><span class="kw">hence </span><a NAME="E13:49_1_2_5_1_1"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:49_1_2_5_1_1"><span class="lab"><font color="Green" title="E65">A56</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2_5_1_2"><span class="kw">suppose </span></a><a NAME="E1:49_1_2_5_1_2"/>
 not 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font></span><br/><div class="add"><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A57</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:49_1_2"><span class="lab"><font color="Green" title="E61">A52</font></span></a>, <a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">XXREAL_0:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">s0</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">q</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c3">p</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:49_1_2"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="euclid.html#T65" title="EUCLID:th.65">EUCLID:65</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">v3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span>, <font color="Maroon" title="c20">v4</font> = <font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> 2 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T22" title="EUCLID:th.22">EUCLID:22</a></span>;<br/><a NAME="E4:49_1_2_5_1_2"/><span class="lab"><font color="Green" title="E63">A58</font></span>: 
<font color="Maroon" title="c10">r0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c10">r0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font>
 ;<br/> <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) = 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">v3</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c20">v4</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="sppol_1.html#T5" target="_self" title="SPPOL_1:th.5">Th20</a></span>
<br/>.= 
<span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T69" title="EUCLID:th.69">EUCLID:69</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_1_2_5_1_2"><span class="lab"><font color="Green" title="E62">A57</font></span></a>, <a class="ref" href="euclid.html#T11" title="EUCLID:th.11">EUCLID:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T67" title="COMPLEX1:th.67">COMPLEX1:67</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <font color="Maroon" title="c10">r0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:49_1_2"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>
<br/>.= 
<font color="Maroon" title="c10">r0</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:49_1_2_5_1_2"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c17">u3</font>,<font color="Maroon" title="c18">u0</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:49"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E4:49_1_2_5_1_2"><span class="lab"><font color="Green" title="E63">A58</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><a NAME="E37:49_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">u3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u6</font> where <font color="Olive" title="b1">u6</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> :  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c18">u0</font>,<font color="Olive" title="b1">u6</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">s</font> </span> } </span> 
 ;<br/><a NAME="E38:49_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c18">u0</font>,<font color="Maroon" title="c7">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T17" title="METRIC_1:th.17">METRIC_1:17</a></span>;<br/><a NAME="E39:49_1_2"/><span class="kw">then </span>
 <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">r0</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,1)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K2" title="SQUARE_1:func.2">max</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">s0</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c10">r0</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p0"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c8">v2</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c9">v1</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c18">u0</font>,<font color="Maroon" title="c7">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:49_1_2"><span class="lab"><font color="Green" title="E60">A51</font></span></a>, <a class="ref" href="topreal3.html#T21" title="TOPREAL3:th.21">TOPREAL3:21</a></span>;<br/><span class="kw">hence </span><a NAME="E40:49_1_2"/>
 ex <font color="Olive" title="b1">p3</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> st <br/>(  not <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K2" title="TOPREAL1:func.2">LSeg</a> (<font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>) &amp; <font color="Olive" title="b1">p3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K9" title="METRIC_1:func.9">Ball</a> (<font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c7">s</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:49"><span class="lab"><font color="Green" title="E34">A4</font></span></a>, <a class="txt" href="#E21:49_1_2"><span class="lab"><font color="Green" title="E54">A38</font></span></a>, <a class="txt" href="#E28:49_1_2"><span class="lab"><font color="Green" title="E57">A41</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
