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<b>let </b><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font>, <font color="Olive" title="b3">s3</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font><br/> for <font color="Olive" title="b4">t1</font>, <font color="Olive" title="b5">t2</font>, <font color="Olive" title="b6">t3</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><br/> for <font color="Olive" title="b7">l1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">s1</font>,<font color="Olive" title="b4">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b8">l2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b3">s3</font>,<font color="Olive" title="b6">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b9">p1</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><br/> for <font color="Olive" title="b10">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Olive" title="b2">s2</font>,<font color="Olive" title="b3">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b1">s1</font>,<font color="Olive" title="b4">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b2">s2</font>,<font color="Olive" title="b5">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Olive" title="b3">s3</font>,<font color="Olive" title="b6">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b9">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b7">l1</font> &amp; <font color="Olive" title="b10">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b8">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b8">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b9">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b10">p2</font></span><br/><b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font>, <font color="Maroon" title="c8">s3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t1</font>, <font color="Olive" title="b2">t2</font>, <font color="Olive" title="b3">t3</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font><br/> for <font color="Olive" title="b4">l1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Olive" title="b1">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b2">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b5">l2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b2">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Olive" title="b3">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b6">p1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font><br/> for <font color="Olive" title="b7">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Olive" title="b1">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b2">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Olive" title="b2">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Olive" title="b3">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b6">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b4">l1</font> &amp; <font color="Olive" title="b7">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b5">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b5">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b6">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b7">p2</font></span><br/><b>let </b><font color="Maroon" title="c9">t1</font>, <font color="Maroon" title="c10">t2</font>, <font color="Maroon" title="c11">t3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b2">l2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b3">p1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font><br/> for <font color="Olive" title="b4">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b3">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b1">l1</font> &amp; <font color="Olive" title="b4">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b2">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b2">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b4">p2</font></span><br/><b>let </b><font color="Maroon" title="c12">l1</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span><br/> for <font color="Olive" title="b2">p1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font><br/> for <font color="Olive" title="b3">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b2">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c12">l1</font> &amp; <font color="Olive" title="b3">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Olive" title="b1">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b1">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b3">p2</font></span><br/><b>let </b><font color="Maroon" title="c13">l2</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p1</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font><br/> for <font color="Olive" title="b2">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Olive" title="b1">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c12">l1</font> &amp; <font color="Olive" title="b2">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c13">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b2">p2</font></span><br/><b>let </b><font color="Maroon" title="c14">p1</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p2</font> being   <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>  st <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c14">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c12">l1</font> &amp; <font color="Olive" title="b1">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c13">l2</font> holds <br/> <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Olive" title="b1">p2</font></span><br/><b>let </b><font color="Maroon" title="c15">p2</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <font color="Maroon" title="c14">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c12">l1</font> &amp; <font color="Maroon" title="c15">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c13">l2</font> implies  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font> )</span><br/>























<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green" title="E26">A1</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green" title="E27">A2</font></i>: 
<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span>,<span class="p1"><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K6" title="BORSUK_1:func.6">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E3:35"/><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon" title="c14">p1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c12">l1</font>
 <b>and </b><br/><a NAME="E4:35"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c15">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <font color="Maroon" title="c13">l2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span><br/>

<a NAME="E5:35"/><i><font color="Green" title="E30">A5</font></i>: 
<font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c7">s2</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="topalg_4.html#T11" target="_self" title="TOPALG_4:th.11">Th11</a></i>;<br/>
<a NAME="E6:35"/><i><font color="Green" title="E31">A6</font></i>: 
<font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c8">s3</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="topalg_4.html#T11" target="_self" title="TOPALG_4:th.11">Th11</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c16">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E1:35_1"/><i><font color="Green" title="E32">A7</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E2:35_1"/><i><font color="Green" title="E33">A8</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c12">l1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E3:35_1"/><i><font color="Green" title="E34">A9</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c13">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_1"/>
( <font color="Maroon" title="c16">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 or <font color="Maroon" title="c16">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1"><b>suppose </b></a><a NAME="E1:35_1_1_1"/><i><font color="Green" title="E35">A10</font></i>: 
<font color="Maroon" title="c16">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:35_1_1_1"/><b>then </b><i><font color="Green" title="E36">A11</font></i>: 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> 
 <b>by </b><i><a class="ref" href="borsuk_6.html#T6" title="BORSUK_6:th.6">BORSUK_6:6</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="#E1:35_1"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="mcart_1.html#D12" title="MCART_1:def.12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font></span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="#E1:35_1_1_1"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="borsuk_2.html#D5" title="BORSUK_2:def.5">BORSUK_2:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c14">p1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:35"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="#E2:35_1"><i><font color="Green" title="E33">A8</font></i></a>, <a class="txt" href="#E2:35_1_1_1"><i><font color="Green" title="E36">A11</font></i></a>, <a class="ref" href="mcart_1.html#D12" title="MCART_1:def.12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font>
<b>by </b><i><a class="txt" href="#E5:35"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="#E6:35"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="#E1:35_1_1_1"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="borsuk_2.html#D5" title="BORSUK_2:def.5">BORSUK_2:def 5</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_2"><b>suppose </b></a><a NAME="E1:35_1_1_2"/><i><font color="Green" title="E35">A12</font></i>: 
<font color="Maroon" title="c16">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:35_1_1_2"/><b>then </b><i><font color="Green" title="E36">A13</font></i>: 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="borsuk_1.html#K19" title="BORSUK_1:func.19">I[01]</a> 
 <b>by </b><i><a class="ref" href="borsuk_6.html#T7" title="BORSUK_6:th.7">BORSUK_6:7</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="#E1:35_1"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="mcart_1.html#D12" title="MCART_1:def.12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">l2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="#E2:35"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="#E1:35_1_1_2"><i><font color="Green" title="E35">A12</font></i></a>, <a class="ref" href="borsuk_2.html#D5" title="BORSUK_2:def.5">BORSUK_2:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c15">p2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c16">x</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="#E4:35"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="#E3:35_1"><i><font color="Green" title="E34">A9</font></i></a>, <a class="txt" href="#E2:35_1_1_2"><i><font color="Green" title="E36">A13</font></i></a>, <a class="ref" href="mcart_1.html#D12" title="MCART_1:def.12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">x</font>
<b>by </b><i><a class="txt" href="#E5:35"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="#E6:35"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="#E1:35_1_1_2"><i><font color="Green" title="E35">A12</font></i></a>, <a class="ref" href="borsuk_2.html#D5" title="BORSUK_2:def.5">BORSUK_2:def 5</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:35"/>
 <a href="topalg_4.html#K4" title="TOPALG_4:func.4">pr1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c14">p1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">p2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
