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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">t1</font>, <font color="Olive" title="b3">t2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b4">s1</font>, <font color="Olive" title="b5">s2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">A</font>, <font color="Olive" title="b7">B</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font><br/>  for <font color="Olive" title="b8">C</font>, <font color="Olive" title="b9">D</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font>  st <font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b6">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b8">C</font> &amp; <font color="Olive" title="b7">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b9">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font>)</span>)</span>,<font color="Olive" title="b8">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Olive" title="b1">S</font>,<font color="Olive" title="b4">s1</font>,<font color="Olive" title="b5">s2</font>)</span>)</span>,<font color="Olive" title="b9">D</font>) holds <br/> <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font>)</span>)</span>,<font color="Olive" title="b6">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font>)</span>)</span>,<font color="Olive" title="b7">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t1</font>, <font color="Olive" title="b2">t2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">s1</font>, <font color="Olive" title="b4">s2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b5">A</font>, <font color="Olive" title="b6">B</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font><br/>  for <font color="Olive" title="b7">C</font>, <font color="Olive" title="b8">D</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font>  st <font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b5">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b7">C</font> &amp; <font color="Olive" title="b6">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b8">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font>)</span>)</span>,<font color="Olive" title="b7">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Olive" title="b3">s1</font>,<font color="Olive" title="b4">s2</font>)</span>)</span>,<font color="Olive" title="b8">D</font>) holds <br/> <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font>)</span>)</span>,<font color="Olive" title="b5">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">t1</font>,<font color="Olive" title="b2">t2</font>)</span>)</span>,<font color="Olive" title="b6">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">t1</font>, <font color="Maroon" title="c4">t2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font><br/>  for <font color="Olive" title="b5">C</font>, <font color="Olive" title="b6">D</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">s2</font>  st <font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b3">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">C</font> &amp; <font color="Olive" title="b4">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b6">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">s2</font>)</span>)</span>,<font color="Olive" title="b5">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">s2</font>)</span>)</span>,<font color="Olive" title="b6">D</font>) holds <br/> <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Olive" title="b3">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Olive" title="b4">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font><br/>  for <font color="Olive" title="b3">C</font>, <font color="Olive" title="b4">D</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>  st <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b1">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b2">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Olive" title="b3">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Olive" title="b4">D</font>) holds <br/> <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Olive" title="b1">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Olive" title="b2">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c7">A</font>, <font color="Maroon" title="c8">B</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C</font>, <font color="Olive" title="b2">D</font> being    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>  st <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c7">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">C</font> &amp; <font color="Maroon" title="c8">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Olive" title="b1">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Olive" title="b2">D</font>) holds <br/> <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c7">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c8">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c9">C</font>, <font color="Maroon" title="c10">D</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c7">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c9">C</font> &amp; <font color="Maroon" title="c8">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c10">D</font> &amp;  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c9">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c10">D</font>) implies  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c7">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c8">B</font>) )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:9"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <span class="kw">and </span><br/><a NAME="E2:9"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <span class="kw">and </span><br/><a NAME="E3:9"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
( <font color="Maroon" title="c7">A</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c9">C</font> &amp; <font color="Maroon" title="c8">B</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c10">D</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c9">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c10">D</font>) or  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c7">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c8">B</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E4:9"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c9">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c5">s1</font>,<font color="Maroon" title="c6">s2</font>)</span>)</span>,<font color="Maroon" title="c10">D</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c7">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c8">B</font>)</span><br/>

<a NAME="E5:9"/><span class="kw">then </span>
<font color="Maroon" title="c9">C</font>,<font color="Maroon" title="c10">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="topalg_1.html#T46" onmouseover="rs('topalg_1/T46')" onmouseout="rh()">TOPALG_1:46</a></span>;<br/>
<a NAME="E6:9"/><span class="kw">then </span>
<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c8">B</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E3:9"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="topalg_6.html#T6" target="_self" onmouseover="rs('topalg_6/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:9"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c7">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="topalg_1.html#K3" title="TOPALG_1:func.3">EqRel</a> (<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c3">t1</font>,<font color="Maroon" title="c4">t2</font>)</span>)</span>,<font color="Maroon" title="c8">B</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="topalg_1.html#T46" onmouseover="rs('topalg_1/T46')" onmouseout="rh()">TOPALG_1:46</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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