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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" 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_4.html#K11" title="TOPALG_4:func.11">FGPrIso</a> (<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>) is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</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" 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_4.html#K11" title="TOPALG_4:func.11">FGPrIso</a> (<font color="Maroon" title="c6">s</font>,<font color="Olive" title="b1">t</font>) is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</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" 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="E1:44"/>
 <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_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a> <a class="txt" 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#V2" title="FUNCT_2:attr.2">onto</a> </span><br/>

<span class="kw">thus </span><a NAME="E2:44"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><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>)</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 <span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p3">(<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="p3">(<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></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a> <a class="txt" 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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