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<span class="kw">let </span><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" 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   <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="b2">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span>), <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c4">S</font>,<font color="Olive" title="b1">s</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c5">T</font>,<font color="Olive" title="b2">t</font>)</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">s</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" 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">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font> holds   <a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">t</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span>), <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c5">T</font>,<font color="Olive" title="b1">t</font>)</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c7">t</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" 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="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c5">T</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">]</a></span>), <a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c6">s</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK6" title="TOPALG_1:NK.6">pi_1</a> (<font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c7">t</font>)</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>







<span class="kw">take </span>
 <a href="topalg_4.html#K11" title="TOPALG_4:func.11">FGPrIso</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>)
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_6.html#D11" onmouseover="rs('group_6/D11')" onmouseout="rh()">GROUP_6:def 11</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">  <a href="topalg_4.html#K11" title="TOPALG_4:func.11">FGPrIso</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>) is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:43"/>
 <a href="topalg_4.html#K11" title="TOPALG_4:func.11">FGPrIso</a> (<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c7">t</font>) is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</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"> verum</span><br/>


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