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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; <font color="Olive" title="b8">C</font>,<font color="Olive" title="b9">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b6">A</font>,<font color="Olive" title="b7">B</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </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; <font color="Olive" title="b7">C</font>,<font color="Olive" title="b8">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">B</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </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; <font color="Olive" title="b5">C</font>,<font color="Olive" title="b6">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </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; <font color="Olive" title="b3">C</font>,<font color="Olive" title="b4">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> </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; <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">D</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a>  holds <br/><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><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; <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>  implies <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><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:8"/><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>  &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>  )
 <span class="kw">and </span><br/><a NAME="E2:8"/><span class="lab"><font color="Green" title="E8">A2</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 <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>  or <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><br/>

<span class="kw">given </span><font color="Maroon" title="c11">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<font color="Maroon" title="c2">S</font><span class="kw"> such that </span><a NAME="E4:8"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
<font color="Maroon" title="c11">f</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">and </span><br/><a NAME="E5:8"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
 for <font color="Olive" title="b1">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c11">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">t</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">C</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c11">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">t</font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">D</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> &amp; <font color="Maroon" title="c11">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive" title="b1">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s1</font> &amp; <font color="Maroon" title="c11">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive" title="b1">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s2</font> )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="borsuk_2.html#D7" onmouseover="rs('borsuk_2/D7')" onmouseout="rh()">BORSUK_2:def 7</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"> <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><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c12">g</font> = <font color="Maroon" title="c11">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a>,<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topreala.html#T7" onmouseover="rs('topreala/T7')" onmouseout="rh()">TOPREALA:7</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c12">g</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="borsuk_2.html#D7" onmouseover="rs('borsuk_2/D7')" onmouseout="rh()">BORSUK_2:def 7</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"> ( <font color="Maroon" title="c12">g</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; (  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t1</font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t2</font> ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E7:8"/>
<font color="Maroon" title="c12">g</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="pre_topc.html#T26" onmouseover="rs('pre_topc/T26')" onmouseout="rh()">PRE_TOPC:26</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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t1</font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t2</font> )</span><br/>

<a NAME="E8:8"/>
( <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c3">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> &amp; <font color="Maroon" title="c4">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="borsuk_2.html#D2" onmouseover="rs('borsuk_2/D2')" onmouseout="rh()">BORSUK_2:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:8"/>
 for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> holds <br/> ( <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive">b<sub>1</sub></font>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t1</font> &amp; <font color="Maroon" title="c12">g</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (1,<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">t2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E10">A4</font></span></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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