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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">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">pp9</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="b8">A</font>, <font color="Olive" title="b9">B</font>, <font color="Olive" title="b10">C</font>, <font color="Olive" title="b11">Q</font>, <font color="Olive" title="b12">O</font>, <font color="Olive" title="b13">O1</font>, <font color="Olive" title="b14">O2</font>, <font color="Olive" title="b15">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="b8">A</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="b9">B</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="b10">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="b10">C</font> &amp; not <font color="Olive" title="b8">A</font>,<font color="Olive" title="b9">B</font>,<font color="Olive" title="b10">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</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">Q</font> &amp; <font color="Olive" title="b8">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b11">Q</font> &amp; <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">O</font> &amp; <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">O</font> &amp; not <font color="Olive" title="b9">B</font>,<font color="Olive" title="b10">C</font>,<font color="Olive" title="b12">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b4">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b10">C</font> &amp; <font color="Olive" title="b4">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b9">B</font> &amp; <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">O1</font> &amp; <font color="Olive" title="b4">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">O1</font> &amp; <font color="Olive" title="b5">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">A</font> &amp; <font color="Olive" title="b5">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b13">O1</font> &amp; <font color="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b12">O</font> &amp; <font color="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">O2</font> &amp; <font color="Olive" title="b5">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">O2</font> &amp; <font color="Olive" title="b7">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">O2</font> &amp; <font color="Olive" title="b4">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">O3</font> &amp; <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">O3</font> &amp; <font color="Olive" title="b7">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b15">O3</font> &amp; <font color="Olive" title="b7">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> &amp; <font color="Olive" title="b6">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> &amp; not <font color="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">A</font> &amp; not <font color="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b11">Q</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b10">C</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">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="b8">A</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b10">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="b11">Q</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b9">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="b8">A</font>,<font color="Olive" title="b6">q</font>,<font color="Olive" title="b11">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">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</font>, <font color="Maroon" title="c8">pp9</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">B</font>, <font color="Olive" title="b3">C</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="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">B</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="b3">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">C</font> &amp; not <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c4">c</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="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; <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; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">O</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">O</font> &amp; not <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b5">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">O1</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">O1</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">O1</font> &amp; <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">O</font> &amp; <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">O2</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">O2</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">O2</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O3</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O3</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O3</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">Q</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; not <font color="Maroon" title="c7">q</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="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">Q</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Olive" title="b3">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b2">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="b3">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="b2">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="c7">q</font>,<font color="Olive" title="b4">Q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">A</font>, <font color="Maroon" title="c10">B</font>, <font color="Maroon" title="c11">C</font>, <font color="Maroon" title="c12">Q</font>, <font color="Maroon" title="c13">O</font>, <font color="Maroon" title="c14">O1</font>, <font color="Maroon" title="c15">O2</font>, <font color="Maroon" title="c16">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="c9">A</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="c10">B</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="c11">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="c11">C</font> &amp; not <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">B</font>,<font color="Maroon" title="c11">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</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">Q</font> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">Q</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">O</font> &amp; <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">O</font> &amp; not <font color="Maroon" title="c10">B</font>,<font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c13">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">C</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">B</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O1</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O1</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O1</font> &amp; <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">O</font> &amp; <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> &amp; <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> &amp; <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; not <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font> &amp; not <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</font> implies <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span> )</span><br/>































<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E11">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="c9">A</font>
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E12">A2</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="c10">B</font>
 <span class="kw">and </span><br/><a NAME="E3:17"/><span class="lab"><font color="Green" title="E13">A3</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">C</font>
 <span class="kw">and </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E14">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="c11">C</font>
 <span class="kw">and </span><br/><a NAME="E5:17"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
not <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c10">B</font>,<font color="Maroon" title="c11">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 <span class="kw">and </span><br/><a NAME="E6:17"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font>
 <span class="kw">and </span><br/><a NAME="E7:17"/><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">C</font>
 <span class="kw">and </span><br/><a NAME="E8:17"/><span class="lab"><font color="Green" title="E18">A8</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</font>
 <span class="kw">and </span><br/><a NAME="E9:17"/><span class="lab"><font color="Green" title="E19">A9</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">Q</font>
 <span class="kw">and </span><br/><a NAME="E10:17"/><span class="lab"><font color="Green" title="E20">A10</font></span>: 
<font color="Maroon" title="c9">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">Q</font>
 <span class="kw">and </span><br/><a NAME="E11:17"/><span class="lab"><font color="Green" title="E21">A11</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="c13">O</font>
 <span class="kw">and </span><br/><a NAME="E12:17"/><span class="lab"><font color="Green" title="E22">A12</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="c13">O</font>
 <span class="kw">and </span><br/><a NAME="E13:17"/><span class="lab"><font color="Green" title="E23">A13</font></span>: 
not <font color="Maroon" title="c10">B</font>,<font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c13">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 <span class="kw">and </span><br/><a NAME="E14:17"/><span class="lab"><font color="Green" title="E24">A14</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">C</font>
 <span class="kw">and </span><br/><a NAME="E15:17"/><span class="lab"><font color="Green" title="E25">A15</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">B</font>
 <span class="kw">and </span><br/><a NAME="E16:17"/><span class="lab"><font color="Green" title="E26">A16</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="c14">O1</font>
 <span class="kw">and </span><br/><a NAME="E17:17"/><span class="lab"><font color="Green" title="E27">A17</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O1</font>
 <span class="kw">and </span><br/><a NAME="E18:17"/><span class="lab"><font color="Green" title="E28">A18</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font>
 <span class="kw">and </span><br/><a NAME="E19:17"/><span class="lab"><font color="Green" title="E29">A19</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O1</font>
 <span class="kw">and </span><br/><a NAME="E20:17"/><span class="lab"><font color="Green" title="E30">A20</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">O</font>
 <span class="kw">and </span><br/><a NAME="E21:17"/><span class="lab"><font color="Green" title="E31">A21</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font>
 <span class="kw">and </span><br/><a NAME="E22:17"/><span class="lab"><font color="Green" title="E32">A22</font></span>: 
( <font color="Maroon" title="c6">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> &amp; <font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> )
 <span class="kw">and </span><br/><a NAME="E23:17"/><span class="lab"><font color="Green" title="E33">A23</font></span>: 
( <font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font> )
 <span class="kw">and </span><br/><a NAME="E24:17"/><span class="lab"><font color="Green" title="E34">A24</font></span>: 
<font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">O3</font>
 <span class="kw">and </span><br/><a NAME="E25:17"/><span class="lab"><font color="Green" title="E35">A25</font></span>: 
<font color="Maroon" title="c8">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</font>
 <span class="kw">and </span><br/><a NAME="E26:17"/><span class="lab"><font color="Green" title="E36">A26</font></span>: 
<font color="Maroon" title="c7">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">and </span><br/><a NAME="E27:17"/><span class="lab"><font color="Green" title="E37">A27</font></span>: 
not <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">A</font>
 <span class="kw">and </span><br/><a NAME="E28:17"/><span class="lab"><font color="Green" title="E38">A28</font></span>: 
not <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c17">f</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">g</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">B</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">g1</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">B</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">f1</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font>;<br/>
<a NAME="E29:17"/><span class="lab"><font color="Green" title="E39">A29</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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="projred2.html#T5" target="_self" title="PROJRED2:th.5">Th5</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">X</font> =  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c9">A</font>;<br/>
<a NAME="E30:17"/><span class="lab"><font color="Green" title="E40">A30</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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">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="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:17"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E38">A28</font></span></a>, <a class="ref" href="projred2.html#T5" target="_self" title="PROJRED2:th.5">Th5</a></span>;<br/>
<a NAME="E31:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A31</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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">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="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="txt" href="#E27:17"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E38">A28</font></span></a>, <a class="ref" href="projred1.html#T25" title="PROJRED1:th.25">PROJRED1:25</a></span>;<br/>
<a NAME="E32:17"/><span class="lab"><font color="Green" title="E42">A32</font></span>: 
<font color="Maroon" title="c14">O1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">O2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_1"/>
not <font color="Maroon" title="c14">O1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">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="E2:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E17:17"><span class="lab"><font color="Green" title="E27">A17</font></span></a>, <a class="txt" href="#E20:17"><span class="lab"><font color="Green" title="E30">A20</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E26:17"><span class="lab"><font color="Green" title="E36">A26</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="E3:17_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:17"><span class="lab"><font color="Green" title="E23">A13</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</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="E33:17"/>
<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>;<br/>
<a NAME="E34:17"/><span class="kw">then </span>
<font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E17:17"><span class="lab"><font color="Green" title="E27">A17</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E29">A19</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E35:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A33</font></span>: 
<font color="Maroon" title="c8">pp9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E10:17"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E25:17"><span class="lab"><font color="Green" title="E35">A25</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E36:17"/><span class="lab"><font color="Green" title="E44">A34</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="c9">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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">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="17_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c22">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="c22">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:17_2"/><span class="lab"><font color="Green" title="E45">A35</font></span>: 
<font color="Maroon" title="c22">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c23">Q3</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="E3:17_2"/><span class="lab"><font color="Green" title="E46">A36</font></span>: 
( <font color="Maroon" title="c7">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c23">Q3</font> &amp; <font color="Maroon" title="c22">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c23">Q3</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="c24">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="E5:17_2"/><span class="lab"><font color="Green" title="E47">A37</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="c24">Q1</font> &amp; <font color="Maroon" title="c22">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c24">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="c25">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="E7:17_2"/><span class="lab"><font color="Green" title="E48">A38</font></span>: 
<font color="Maroon" title="c25">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c23">Q3</font>
 <span class="kw">and </span><br/><a NAME="E8:17_2"/><span class="lab"><font color="Green" title="E49">A39</font></span>: 
<font color="Maroon" title="c25">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">Q</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/>
<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="E10:17_2"/><span class="lab"><font color="Green" title="E50">A40</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="c24">Q1</font>
 <span class="kw">and </span><br/><a NAME="E11:17_2"/><span class="lab"><font color="Green" title="E51">A41</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="c11">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/>
<div><span class="lab"><font color="Green" title="E52">A42</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:17_2_1"/><span class="lab"><font color="Green" title="E53">A43</font></span>: 
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">pp9</font>,<font color="Maroon" title="c25">y</font>,<font color="Maroon" title="c4">c</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">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="c5">d</font>,<font color="Maroon" title="c26">x9</font>,<font color="Maroon" title="c4">c</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">C</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E25:17"><span class="lab"><font color="Green" title="E35">A25</font></span></a>, <a class="txt" href="#E11:17_2"><span class="lab"><font color="Green" title="E51">A41</font></span></a>, <a class="txt" href="#E8:17_2"><span class="lab"><font color="Green" title="E49">A39</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E2:17_2_1"/><span class="lab"><font color="Green" title="E54">A44</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">p</font>,<font color="Maroon" title="c8">pp9</font>,<font color="Maroon" title="c7">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="c15">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="c8">pp9</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</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">O3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E32">A22</font></span></a>, <a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E33">A23</font></span></a>, <a class="txt" href="#E24:17"><span class="lab"><font color="Green" title="E34">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="E3:17_2_1"/><span class="lab"><font color="Green" title="E55">A45</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="c2">a</font>,<font color="Maroon" title="c7">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="c13">O</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c25">y</font>,<font color="Maroon" title="c7">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="c23">Q3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E22">A12</font></span></a>, <a class="txt" href="#E20:17"><span class="lab"><font color="Green" title="E30">A20</font></span></a>, <a class="txt" href="#E3:17_2"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="txt" href="#E7:17_2"><span class="lab"><font color="Green" title="E48">A38</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E4:17_2_1"/><span class="lab"><font color="Green" title="E56">A46</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">p</font>,<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c4">c</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="c9">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">p</font>,<font color="Maroon" title="c5">d</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="c14">O1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E17:17"><span class="lab"><font color="Green" title="E27">A17</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E29">A19</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</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">assume </span><a NAME="E5:17_2_1"/><span class="lab"><font color="Green" title="E57">A47</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">x</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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font></span><br/><a NAME="E6:17_2_1"/>
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c26">x9</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="c24">Q1</font> &amp; <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c14">O1</font>,<font color="Maroon" title="c15">O2</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="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E27:17"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E32:17"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E5:17_2"><span class="lab"><font color="Green" title="E47">A37</font></span></a>, <a class="txt" href="#E10:17_2"><span class="lab"><font color="Green" title="E50">A40</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">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="E8:17_2_1"/><span class="lab"><font color="Green" title="E58">A48</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c25">y</font>,<font color="Maroon" title="c26">x9</font>,<font color="Maroon" title="c3">b</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">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E35:17"><span class="lab"><font color="Green" title="E43">A33</font></span></a>, <a class="txt" href="#E5:17_2_1"><span class="lab"><font color="Green" title="E57">A47</font></span></a>, <a class="txt" href="#E4:17_2_1"><span class="lab"><font color="Green" title="E56">A46</font></span></a>, <a class="txt" href="#E2:17_2_1"><span class="lab"><font color="Green" title="E54">A44</font></span></a>, <a class="txt" href="#E1:17_2_1"><span class="lab"><font color="Green" title="E53">A43</font></span></a>, <a class="txt" href="#E3:17_2_1"><span class="lab"><font color="Green" title="E55">A45</font></span></a>, <a class="ref" href="projred1.html#T14" title="PROJRED1:th.14">PROJRED1:14</a></span>;<br/><a NAME="E9:17_2_1"/><span class="lab"><font color="Green" title="E59">A49</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">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:17_2_1"><span class="lab"><font color="Green" title="E58">A48</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="c28">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="E11:17_2_1"/><span class="lab"><font color="Green" title="E60">A50</font></span>: 
( <font color="Maroon" title="c28">x99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">R</font> &amp; <font color="Maroon" title="c28">x99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c10">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="E12:17_2_1"/>
<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">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:17_2_1"><span class="lab"><font color="Green" title="E58">A48</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E13:17_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A51</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c28">x99</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E11:17_2"><span class="lab"><font color="Green" title="E51">A41</font></span></a>, <a class="txt" href="#E11:17_2_1"><span class="lab"><font color="Green" title="E60">A50</font></span></a>, <a class="txt" href="#E9:17_2_1"><span class="lab"><font color="Green" title="E59">A49</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/><a NAME="E14:17_2_1"/><span class="lab"><font color="Green" title="E62">A52</font></span>: 
<font color="Maroon" title="c22">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:17"><span class="lab"><font color="Green" title="E40">A30</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a></span>;<br/><a NAME="E15:17_2_1"/>
<font color="Maroon" title="c25">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c27">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:17_2_1"><span class="lab"><font color="Green" title="E58">A48</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E16:17_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A53</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">x99</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="txt" href="#E8:17_2"><span class="lab"><font color="Green" title="E49">A39</font></span></a>, <a class="txt" href="#E11:17_2_1"><span class="lab"><font color="Green" title="E60">A50</font></span></a>, <a class="txt" href="#E9:17_2_1"><span class="lab"><font color="Green" title="E59">A49</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/><a NAME="E17:17_2_1"/><span class="lab"><font color="Green" title="E64">A54</font></span>: 
<font color="Maroon" title="c22">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E39">A29</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a></span>;<br/><a NAME="E18:17_2_1"/>
( <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">x9</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E27:17"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E38">A28</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a>, <a class="txt" href="#E5:17_2"><span class="lab"><font color="Green" title="E47">A37</font></span></a>, <a class="txt" href="#E10:17_2"><span class="lab"><font color="Green" title="E50">A40</font></span></a>, <a class="txt" href="#E11:17_2"><span class="lab"><font color="Green" title="E51">A41</font></span></a>, <a class="txt" href="#E3:17_2"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="txt" href="#E7:17_2"><span class="lab"><font color="Green" title="E48">A38</font></span></a>, <a class="txt" href="#E8:17_2"><span class="lab"><font color="Green" title="E49">A39</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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font> = 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:17_2_1"><span class="lab"><font color="Green" title="E61">A51</font></span></a>, <a class="txt" href="#E16:17_2_1"><span class="lab"><font color="Green" title="E63">A53</font></span></a>, <a class="txt" href="#E17:17_2_1"><span class="lab"><font color="Green" title="E64">A54</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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:17_2_1"><span class="lab"><font color="Green" title="E62">A52</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="E20:17_2_1"/>
<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">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:17_2_2"/><span class="lab"><font color="Green" title="E53">A55</font></span>: 
( <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">pp9</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">pp9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E21:17"><span class="lab"><font color="Green" title="E31">A21</font></span></a>, <a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E32">A22</font></span></a>, <a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E33">A23</font></span></a>, <a class="txt" href="#E24:17"><span class="lab"><font color="Green" title="E34">A24</font></span></a>, <a class="txt" href="#E25:17"><span class="lab"><font color="Green" title="E35">A25</font></span></a>, <a class="txt" href="#E27:17"><span class="lab"><font color="Green" title="E37">A27</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E38">A28</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E2:17_2_2"/><span class="lab"><font color="Green" title="E54">A56</font></span>: 
<font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">x</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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font></span><br/><a NAME="E3:17_2_2"/><span class="lab"><font color="Green" title="E55">A57</font></span>: 
<font color="Maroon" title="c22">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:17"><span class="lab"><font color="Green" title="E40">A30</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a></span>;<br/><a NAME="E4:17_2_2"/><span class="lab"><font color="Green" title="E56">A58</font></span>: 
<font color="Maroon" title="c22">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E39">A29</font></span></a>, <a class="txt" href="#E1:17_2"><span class="lab"><font color="Green" title="E45">A35</font></span></a></span>;<br/><a NAME="E5:17_2_2"/>
( <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E25">A15</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E26">A16</font></span></a>, <a class="txt" href="#E17:17"><span class="lab"><font color="Green" title="E27">A17</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E28">A18</font></span></a>, <a class="txt" href="#E19:17"><span class="lab"><font color="Green" title="E29">A19</font></span></a>, <a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E33">A23</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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font> = 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_2_2"><span class="lab"><font color="Green" title="E54">A56</font></span></a>, <a class="txt" href="#E1:17_2_2"><span class="lab"><font color="Green" title="E53">A55</font></span></a>, <a class="txt" href="#E4:17_2_2"><span class="lab"><font color="Green" title="E56">A58</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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_2_2"><span class="lab"><font color="Green" title="E55">A57</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="E7:17_2_2"/>
<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">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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>
<span class="kw">hence </span><a NAME="E14:17_2"/>
<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">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17_2"><span class="lab"><font color="Green" title="E52">A42</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>
<div><span class="lab"><font color="Green" title="E45">A59</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c22">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="c22">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="c9">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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:17_3"/>
<font color="Maroon" title="c22">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="c9">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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">y</font></span><br/><a NAME="E2:17_3"/><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="c22">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="c9">A</font> )
 ;<br/><span class="kw">hence </span><a NAME="E3:17_3"/>
<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">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">C</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:17"><span class="lab"><font color="Green" title="E44">A34</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="E38:17"/>
 <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="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c9">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E29:17"><span class="lab"><font color="Green" title="E39">A29</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="E39:17"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> <font color="Maroon" title="c11">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c11">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="c12">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">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="c9">A</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c12">Q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:17"><span class="lab"><font color="Green" title="E41">A31</font></span></a>, <a class="txt" href="#E37:17"><span class="lab"><font color="Green" title="E45">A59</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/>


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