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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">H1</font>;<br/><b>let </b><font color="Maroon" title="c6">g</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c4">H2</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c5">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green" title="E7">A2</font></i>: 
<font color="Maroon" title="c6">g</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c7">h</font> =  <a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font>;<br/>
<b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E3:5"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c10">a1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c11">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E5:5"/><i><font color="Green" title="E8">A3</font></i>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K17" title="GROUP_7:func.17">&lt;*</a><span class="default"><font color="Maroon" title="c10">a1</font>,<font color="Maroon" title="c11">a2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E6:5"/><i><font color="Green" title="E9">A4</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K17" title="GROUP_7:func.17">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a2</font></span>)</span></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topalg_4.html#D1" target="_self" title="TOPALG_4:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E7:5"/>
<font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c12">b1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c13">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E9:5"/><i><font color="Green" title="E10">A5</font></i>: 
<font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K17" title="GROUP_7:func.17">&lt;*</a><span class="default"><font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">b2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E10:5"/><i><font color="Green" title="E11">A6</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K17" title="GROUP_7:func.17">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">b2</font></span>)</span></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="topalg_4.html#D1" target="_self" title="TOPALG_4:def.1">Def1</a></i>;<br/>
<a NAME="E11:5"/><i><font color="Green" title="E12">A7</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</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 <font color="Maroon" title="c1">G1</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">g</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 <font color="Maroon" title="c2">G2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>assume </b><a NAME="E12:5"/>
<span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" title="TOPALG_4:func.1">Gr2Iso</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">b</font>
 ;<br/>

<a NAME="E13:5"/><b>then </b>
( <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">b2</font> )
 
<b>by </b><i><a class="txt" href="topalg_4.html#E6:5"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="topalg_4.html#E10:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="ref" href="group_7.html#T2" title="GROUP_7:th.2">GROUP_7:2</a></i>;<br/>
<a NAME="E14:5"/><b>then </b>
( <font color="Maroon" title="c10">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b1</font> &amp; <font color="Maroon" title="c11">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b2</font> )
 
<b>by </b><i><a class="txt" href="topalg_4.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="topalg_4.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="topalg_4.html#E11:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E15:5"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="txt" href="topalg_4.html#E5:5"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="topalg_4.html#E9:5"><i><font color="Green" title="E10">A5</font></i></a></i>;<br/>


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