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<span class="kw">let </span><font color="Maroon" title="c1">IPP</font> be   <a href="incproj.html#V5" title="INCPROJ:attr.5">2-dimensional</a>   <a href="incproj.html#V9" title="INCPROJ:attr.9">Desarguesian</a>  <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">o</font>, <font color="Olive" title="b6">o99</font>, <font color="Olive" title="b7">d</font>, <font color="Olive" title="b8">o9</font>, <font color="Olive" title="b9">oo9</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><br/> for <font color="Olive" title="b10">A</font>, <font color="Olive" title="b11">C</font>, <font color="Olive" title="b12">B</font>, <font color="Olive" title="b13">Q</font>, <font color="Olive" title="b14">O</font>, <font color="Olive" title="b15">O1</font>, <font color="Olive" title="b16">O2</font>, <font color="Olive" title="b17">O3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st not <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b10">A</font> &amp; not <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">C</font> &amp; not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">B</font> &amp; not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">C</font> &amp; not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">Q</font> &amp; not <font color="Olive" title="b10">A</font>,<font color="Olive" title="b12">B</font>,<font color="Olive" title="b11">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b10">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b13">Q</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b10">A</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">o</font>,<font color="Olive" title="b6">o99</font>,<font color="Olive" title="b7">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b12">B</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">c</font>,<font color="Olive" title="b7">d</font>,<font color="Olive" title="b8">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b11">C</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b7">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b14">O</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b4">c</font>,<font color="Olive" title="b9">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b13">Q</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">o</font>,<font color="Olive" title="b8">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b15">O1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b8">o9</font>,<font color="Olive" title="b9">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b16">O2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">o</font>,<font color="Olive" title="b9">oo9</font>,<font color="Olive" title="b3">q</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b17">O3</font> &amp; <font color="Olive" title="b3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">O</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b11">C</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b12">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b10">A</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b11">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b13">Q</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b12">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b10">A</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b13">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">q</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">o</font>, <font color="Maroon" title="c7">o99</font>, <font color="Maroon" title="c8">d</font>, <font color="Maroon" title="c9">o9</font>, <font color="Maroon" title="c10">oo9</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">C</font>, <font color="Olive" title="b3">B</font>, <font color="Olive" title="b4">Q</font>, <font color="Olive" title="b5">O</font>, <font color="Olive" title="b6">O1</font>, <font color="Olive" title="b7">O2</font>, <font color="Olive" title="b8">O3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">C</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">B</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">C</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">Q</font> &amp; not <font color="Olive" title="b1">A</font>,<font color="Olive" title="b3">B</font>,<font color="Olive" title="b2">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font> &amp; <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">Q</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b1">A</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">o99</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b3">B</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">d</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b2">C</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b5">O</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b4">Q</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b6">O1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b7">O2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">oo9</font>,<font color="Maroon" title="c4">q</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b8">O3</font> &amp; <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">O</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b2">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b3">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b4">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b3">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b1">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Olive" title="b4">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c11">A</font>, <font color="Maroon" title="c12">C</font>, <font color="Maroon" title="c13">B</font>, <font color="Maroon" title="c14">Q</font>, <font color="Maroon" title="c15">O</font>, <font color="Maroon" title="c16">O1</font>, <font color="Maroon" title="c17">O2</font>, <font color="Maroon" title="c18">O3</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font> &amp; not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font> &amp; not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font> &amp; not <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c13">B</font>,<font color="Maroon" title="c12">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">q</font> &amp; <font color="Maroon" title="c11">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Q</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c11">A</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">o99</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c13">B</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">d</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c12">C</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c15">O</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c14">Q</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c16">O1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c17">O2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">oo9</font>,<font color="Maroon" title="c4">q</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">O3</font> &amp; <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font> implies <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span> )</span><br/>



































<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 <span class="kw">and </span><br/><a NAME="E2:18"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 <span class="kw">and </span><br/><a NAME="E3:18"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font>
 <span class="kw">and </span><br/><a NAME="E4:18"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 <span class="kw">and </span><br/><a NAME="E5:18"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 <span class="kw">and </span><br/><a NAME="E6:18"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
not <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c13">B</font>,<font color="Maroon" title="c12">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 <span class="kw">and </span><br/><a NAME="E7:18"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">and </span><br/><a NAME="E8:18"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c3">b</font> <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="E9:18"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c11">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Q</font>
 <span class="kw">and </span><br/><a NAME="E10:18"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c11">A</font>
 <span class="kw">and </span><br/><a NAME="E11:18"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c7">o99</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c13">B</font>
 <span class="kw">and </span><br/><a NAME="E12:18"/><span class="lab"><font color="Green" title="E23">A12</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c8">d</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c12">C</font>
 <span class="kw">and </span><br/><a NAME="E13:18"/><span class="lab"><font color="Green" title="E24">A13</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c8">d</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c15">O</font>
 <span class="kw">and </span><br/><a NAME="E14:18"/><span class="lab"><font color="Green" title="E25">A14</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c14">Q</font>
 <span class="kw">and </span><br/><a NAME="E15:18"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c9">o9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c16">O1</font>
 <span class="kw">and </span><br/><a NAME="E16:18"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c17">O2</font>
 <span class="kw">and </span><br/><a NAME="E17:18"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c10">oo9</font>,<font color="Maroon" title="c4">q</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">O3</font>
 <span class="kw">and </span><br/><a NAME="E18:18"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span><br/>

<a NAME="E19:18"/><span class="lab"><font color="Green" title="E30">A19</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E20:18"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
( <font color="Maroon" title="c5">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font> &amp; <font color="Maroon" title="c5">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E21:18"/><span class="lab"><font color="Green" title="E32">A21</font></span>: 
<font color="Maroon" title="c9">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E22:18"/><span class="lab"><font color="Green" title="E33">A22</font></span>: 
<font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E23:18"/><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E24:18"/><span class="lab"><font color="Green" title="E35">A24</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E25:18"/><span class="lab"><font color="Green" title="E36">A25</font></span>: 
( <font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font> &amp; <font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">X</font> =  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">f</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">g</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c22">f1</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">g1</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font>;<br/>
<a NAME="E26:18"/><span class="lab"><font color="Green" title="E37">A26</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E27:18"/><span class="lab"><font color="Green" title="E38">A27</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="projred2.html#T5" target="_self" title="PROJRED2:th.5">Th5</a></span>;<br/>
<a NAME="E28:18"/><span class="lab"><font color="Green" title="E39">A28</font></span>: 
<font color="Maroon" title="c9">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E29:18"/><span class="lab"><font color="Green" title="E40">A29</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E30:18"/><span class="lab"><font color="Green" title="E41">A30</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E31:18"/><span class="lab"><font color="Green" title="E42">A31</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E32:18"/><span class="lab"><font color="Green" title="E43">A32</font></span>: 
<font color="Maroon" title="c8">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E33:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A33</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E19:18"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E31:18"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>;<br/>
<a NAME="E34:18"/><span class="lab"><font color="Green" title="E45">A34</font></span>: 
<font color="Maroon" title="c8">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E35:18"/><span class="lab"><font color="Green" title="E46">A35</font></span>: 
( <font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font> &amp; <font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">O3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E36:18"/><span class="lab"><font color="Green" title="E47">A36</font></span>: 
<font color="Maroon" title="c9">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E37:18"/><span class="lab"><font color="Green" title="E48">A37</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E38:18"/><span class="lab"><font color="Green" title="E49">A38</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E39:18"/><span class="lab"><font color="Green" title="E50">A39</font></span>: 
<font color="Maroon" title="c8">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E40:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A40</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E18:18"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E31:18"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E34:18"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E33:18"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E41:18"/><span class="lab"><font color="Green" title="E52">A41</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E42:18"/><span class="lab"><font color="Green" title="E53">A42</font></span>: 
<font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E43:18"/><span class="lab"><font color="Green" title="E54">A43</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:18"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E44:18"/><span class="lab"><font color="Green" title="E55">A44</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E45:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A45</font></span>: 
<font color="Maroon" title="c6">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E31:18"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="txt" href="#E41:18"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>;<br/>
<a NAME="E46:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A46</font></span>: 
<font color="Maroon" title="c9">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E44:18"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="txt" href="#E19:18"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E43:18"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E36:18"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E47:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A47</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">oo9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E41:18"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E30:18"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E28:18"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="txt" href="#E22:18"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E48:18"/><span class="lab"><font color="Green" title="E59">A48</font></span>: 
not <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:18_1"/>
<font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:18_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:18"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="txt" href="#E35:18"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="txt" href="#E29:18"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="txt" href="#E40:18"><span class="lab"><font color="Green" title="E51">A40</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E20:18"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E42:18"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="txt" href="#E47:18"><span class="lab"><font color="Green" title="E58">A47</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E49:18"/><span class="lab"><font color="Green" title="E60">A49</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E50:18"/>
<font color="Maroon" title="c9">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:18_2"/>
not <font color="Maroon" title="c9">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:18_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">O1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E32:18"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E49:18"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="txt" href="#E34:18"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E36:18"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E31:18"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="txt" href="#E39:18"><span class="lab"><font color="Green" title="E50">A39</font></span></a>, <a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E34:18"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E43:18"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E33:18"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E51:18"/><span class="kw">then </span>
<font color="Maroon" title="c15">O</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E32:18"><span class="lab"><font color="Green" title="E43">A32</font></span></a>, <a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E49:18"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="txt" href="#E34:18"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E28:18"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E52:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A50</font></span>: 
<font color="Maroon" title="c4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">oo9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E18:18"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E30:18"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E22:18"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E53:18"/><span class="lab"><font color="Green" title="E62">A51</font></span>: 
not <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:18_3"/>
<font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:18_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:18"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="txt" href="#E35:18"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="txt" href="#E29:18"><span class="lab"><font color="Green" title="E40">A29</font></span></a>, <a class="txt" href="#E52:18"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E20:18"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E37:18"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="txt" href="#E45:18"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E54:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A52</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:18"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="projred2.html#T5" target="_self" title="PROJRED2:th.5">Th5</a></span>;<br/>
<a NAME="E55:18"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A53</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E48:18"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E53:18"><span class="lab"><font color="Green" title="E62">A51</font></span></a>, <a class="ref" href="projred1.html#T25" title="PROJRED1:th.25">PROJRED1:25</a></span>;<br/>
<a NAME="E56:18"/><span class="lab"><font color="Green" title="E65">A54</font></span>: 
( <font color="Maroon" title="c8">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font> &amp; <font color="Maroon" title="c8">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E57:18"/><span class="lab"><font color="Green" title="E66">A55</font></span>: 
<font color="Maroon" title="c16">O1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">O2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:18_4"/>
not <font color="Maroon" title="c16">O1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">O2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:18_4"/><span class="kw">then </span>
<font color="Maroon" title="c6">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E49:18"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E43:18"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E30:18"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E3:18_4"/><span class="kw">then </span>
<font color="Maroon" title="c15">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:18"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="txt" href="#E26:18"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="txt" href="#E33:18"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:18_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E58:18"/><span class="lab"><font color="Green" title="E67">A56</font></span>: 
( <font color="Maroon" title="c5">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font> &amp; <font color="Maroon" title="c10">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:18"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="ref" href="incsp_1.html#T11" title="INCSP_1:th.11">INCSP_1:11</a></span>;<br/>
<a NAME="E59:18"/><span class="lab"><font color="Green" title="E68">A57</font></span>: 
for <font color="Olive" title="b1">x</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>  st <font color="Olive" title="b1">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_5"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:18_5"/><span class="lab"><font color="Green" title="E69">A58</font></span>: 
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c17">O2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c16">O1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E43:18"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E36:18"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E30:18"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E28:18"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="txt" href="#E22:18"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E2:18_5"/><span class="lab"><font color="Green" title="E70">A59</font></span>: 
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">O3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c15">O</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:18"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E49:18"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="txt" href="#E23:18"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E25:18"><span class="lab"><font color="Green" title="E36">A25</font></span></a>, <a class="txt" href="#E24:18"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E3:18_5"/><span class="lab"><font color="Green" title="E71">A60</font></span>: 
<font color="Maroon" title="c17">O2</font>,<font color="Maroon" title="c16">O1</font>,<font color="Maroon" title="c12">C</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E38:18"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E30:18"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E57:18"><span class="lab"><font color="Green" title="E66">A55</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c24">x</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c24">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:18_5"/><span class="lab"><font color="Green" title="E72">A61</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font></span><br/>

<a NAME="E5:18_5"/><span class="lab"><font color="Green" title="E73">A62</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">o</font>,<font color="Maroon" title="c24">x</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:18"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="txt" href="#E19:18"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E72">A61</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E6:18_5"/><span class="lab"><font color="Green" title="E74">A63</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:18"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E72">A61</font></span></a></span>;<br/>
<a NAME="E7:18_5"/><span class="lab"><font color="Green" title="E75">A64</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:18"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E72">A61</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c25">Q1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E9:18_5"/><span class="lab"><font color="Green" title="E76">A65</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c25">Q1</font> &amp; <font color="Maroon" title="c24">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c25">Q1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c26">x9</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E11:18_5"/><span class="lab"><font color="Green" title="E77">A66</font></span>: 
<font color="Maroon" title="c26">x9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c25">Q1</font>
 <span class="kw">and </span><br/><a NAME="E12:18_5"/><span class="lab"><font color="Green" title="E78">A67</font></span>: 
<font color="Maroon" title="c26">x9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D14" title="INCPROJ:def.14">INCPROJ:def 14</a></span>;<br/>
<a NAME="E13:18_5"/><span class="lab"><font color="Green" title="E79">A68</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c24">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c26">x9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c25">Q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18_5"><span class="lab"><font color="Green" title="E76">A65</font></span></a>, <a class="txt" href="#E11:18_5"><span class="lab"><font color="Green" title="E77">A66</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E14:18_5"/><span class="lab"><font color="Green" title="E80">A69</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">o9</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c26">x9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c12">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:18"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E12:18_5"><span class="lab"><font color="Green" title="E78">A67</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c27">Q2</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E16:18_5"/><span class="lab"><font color="Green" title="E81">A70</font></span>: 
<font color="Maroon" title="c26">x9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">Q2</font>
 <span class="kw">and </span><br/><a NAME="E17:18_5"/><span class="lab"><font color="Green" title="E82">A71</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">Q2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c28">y</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E19:18_5"/><span class="lab"><font color="Green" title="E83">A72</font></span>: 
<font color="Maroon" title="c28">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">Q</font>
 <span class="kw">and </span><br/><a NAME="E20:18_5"/><span class="lab"><font color="Green" title="E84">A73</font></span>: 
<font color="Maroon" title="c28">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">Q2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D14" title="INCPROJ:def.14">INCPROJ:def 14</a></span>;<br/>
<a NAME="E21:18_5"/><span class="lab"><font color="Green" title="E85">A74</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c28">y</font>,<font color="Maroon" title="c10">oo9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c14">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:18"><span class="lab"><font color="Green" title="E67">A56</font></span></a>, <a class="txt" href="#E19:18_5"><span class="lab"><font color="Green" title="E83">A72</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E22:18_5"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c28">y</font>,<font color="Maroon" title="c26">x9</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c27">Q2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:18_5"><span class="lab"><font color="Green" title="E81">A70</font></span></a>, <a class="txt" href="#E17:18_5"><span class="lab"><font color="Green" title="E82">A71</font></span></a>, <a class="txt" href="#E20:18_5"><span class="lab"><font color="Green" title="E84">A73</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">R</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E24:18_5"/><span class="lab"><font color="Green" title="E86">A75</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c28">y</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c24">x</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c29">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E19:18"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E21:18"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E46:18"><span class="lab"><font color="Green" title="E57">A46</font></span></a>, <a class="txt" href="#E1:18_5"><span class="lab"><font color="Green" title="E69">A58</font></span></a>, <a class="txt" href="#E14:18_5"><span class="lab"><font color="Green" title="E80">A69</font></span></a>, <a class="txt" href="#E5:18_5"><span class="lab"><font color="Green" title="E73">A62</font></span></a>, <a class="txt" href="#E21:18_5"><span class="lab"><font color="Green" title="E85">A74</font></span></a>, <a class="txt" href="#E13:18_5"><span class="lab"><font color="Green" title="E79">A68</font></span></a>, <a class="txt" href="#E2:18_5"><span class="lab"><font color="Green" title="E70">A59</font></span></a>, <a class="txt" href="#E3:18_5"><span class="lab"><font color="Green" title="E71">A60</font></span></a>, <a class="ref" href="projred1.html#T14" title="PROJRED1:th.14">PROJRED1:14</a></span>;<br/>
<a NAME="E25:18_5"/><span class="lab"><font color="Green" title="E87">A76</font></span>: 
<font color="Maroon" title="c24">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c29">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:18_5"><span class="lab"><font color="Green" title="E86">A75</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E26:18_5"/>
( <font color="Maroon" title="c28">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c29">R</font> &amp; <font color="Maroon" title="c4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c29">R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:18_5"><span class="lab"><font color="Green" title="E86">A75</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E27:18_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A77</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:18"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E53:18"><span class="lab"><font color="Green" title="E62">A51</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E72">A61</font></span></a>, <a class="txt" href="#E19:18_5"><span class="lab"><font color="Green" title="E83">A72</font></span></a>, <a class="txt" href="#E25:18_5"><span class="lab"><font color="Green" title="E87">A76</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c30">x99</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E29:18_5"/><span class="lab"><font color="Green" title="E89">A78</font></span>: 
( <font color="Maroon" title="c30">x99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">Q2</font> &amp; <font color="Maroon" title="c30">x99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">B</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D14" title="INCPROJ:def.14">INCPROJ:def 14</a></span>;<br/>
<a NAME="E30:18_5"/><span class="lab"><font color="Green" title="E90">A79</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c28">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">x99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:18"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E17:18_5"><span class="lab"><font color="Green" title="E82">A71</font></span></a>, <a class="txt" href="#E29:18_5"><span class="lab"><font color="Green" title="E89">A78</font></span></a>, <a class="txt" href="#E19:18_5"><span class="lab"><font color="Green" title="E83">A72</font></span></a>, <a class="txt" href="#E20:18_5"><span class="lab"><font color="Green" title="E84">A73</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<a NAME="E31:18_5"/><span class="lab"><font color="Green" title="E91">A80</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">x99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E12:18_5"><span class="lab"><font color="Green" title="E78">A67</font></span></a>, <a class="txt" href="#E16:18_5"><span class="lab"><font color="Green" title="E81">A70</font></span></a>, <a class="txt" href="#E17:18_5"><span class="lab"><font color="Green" title="E82">A71</font></span></a>, <a class="txt" href="#E29:18_5"><span class="lab"><font color="Green" title="E89">A78</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<a NAME="E32:18_5"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:18_5"><span class="lab"><font color="Green" title="E72">A61</font></span></a>, <a class="txt" href="#E9:18_5"><span class="lab"><font color="Green" title="E76">A65</font></span></a>, <a class="txt" href="#E11:18_5"><span class="lab"><font color="Green" title="E77">A66</font></span></a>, <a class="txt" href="#E12:18_5"><span class="lab"><font color="Green" title="E78">A67</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> = 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:18_5"><span class="lab"><font color="Green" title="E91">A80</font></span></a>, <a class="txt" href="#E27:18_5"><span class="lab"><font color="Green" title="E88">A77</font></span></a>, <a class="txt" href="#E30:18_5"><span class="lab"><font color="Green" title="E90">A79</font></span></a>, <a class="txt" href="#E7:18_5"><span class="lab"><font color="Green" title="E75">A64</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18_5"><span class="lab"><font color="Green" title="E74">A63</font></span></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E34:18_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E69">A81</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c24">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:18_6"/>
<font color="Maroon" title="c24">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font></span><br/><a NAME="E2:18_6"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Maroon" title="c24">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">A</font> )
 ;<br/><span class="kw">hence </span><a NAME="E3:18_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:18"><span class="lab"><font color="Green" title="E68">A57</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E61:18"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c11">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E27:18"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="ref" href="projred1.html#T25" title="PROJRED1:th.25">PROJRED1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E62:18"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c14">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c13">B</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">A</font>,<font color="Maroon" title="c4">q</font>,<font color="Maroon" title="c14">Q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:18"><span class="lab"><font color="Green" title="E64">A53</font></span></a>, <a class="txt" href="#E60:18"><span class="lab"><font color="Green" title="E69">A81</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
