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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="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</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="E1:6"/><i><font color="Green" title="E7">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</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="c3">H1</font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green" title="E8">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</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="c4">H2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</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>thus </b><a NAME="E3:6"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</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="tarski.html#R1" title="TARSKI:pred.1">c=</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="group_7.html#K11" title="GROUP_7:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font></span><a href="group_7.html#K11" title="GROUP_7:func.11">*&gt;</a></span></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>,<a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a><br/>

<b>let </b><font color="Maroon" title="c8">a</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:6"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="group_7.html#K11" title="GROUP_7:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font></span><a href="group_7.html#K11" title="GROUP_7:func.11">*&gt;</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c9">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c10">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">H2</font><b> such that </b><br/><a NAME="E6:6"/><i><font color="Green" title="E9">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="c9">x</font>,<font color="Maroon" title="c10">y</font></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#T1" target="_self" title="TOPALG_4:th.1">Th1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">a1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:6"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c11">a1</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> <font color="Maroon" title="c5">f</font>
 <b>and </b><br/><a NAME="E9:6"/><i><font color="Green" title="E11">A5</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="txt" href="topalg_4.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">a2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E11:6"/><i><font color="Green" title="E12">A6</font></i>: 
<font color="Maroon" title="c12">a2</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> <font color="Maroon" title="c6">g</font>
 <b>and </b><br/><a NAME="E12:6"/><i><font color="Green" title="E13">A7</font></i>: 
<font color="Maroon" title="c6">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">y</font>
 <b>by </b><i><a class="txt" href="topalg_4.html#E2:6"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E13:6"/><i><font color="Green" title="E14">A8</font></i>: 
 <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> <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="group_7.html#K11" title="GROUP_7:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font></span><a href="group_7.html#K11" title="GROUP_7:func.11">*&gt;</a></span></span>)</span>
 
<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="E14:6"/>
for <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G1</font><br/> for <font color="Olive" title="b2">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G2</font> holds  <span class="p1"><a href="group_7.html#K17" title="GROUP_7:func.17">&lt;*</a><span class="default"><font color="Olive" title="b1">g</font>,<font color="Olive" title="b2">h</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="group_7.html#K11" title="GROUP_7:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font></span><a href="group_7.html#K11" title="GROUP_7:func.11">*&gt;</a></span></span>)</span>
 
;<br/>
<a NAME="E15:6"/><b>then </b><i><font color="Green" title="E15">A9</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c12">a2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <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>
 
<b>by </b><i><a class="txt" href="topalg_4.html#E8:6"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="topalg_4.html#E11:6"><i><font color="Green" title="E12">A6</font></i></a>, <a class="txt" href="topalg_4.html#E13:6"><i><font color="Green" title="E14">A8</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">k1</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="c14">k2</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="E17:6"/><i><font color="Green" title="E16">A10</font></i>: 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c12">a2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <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="c13">k1</font>,<font color="Maroon" title="c14">k2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:6"/><i><font color="Green" title="E17">A11</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> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c12">a2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <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="c13">k1</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="c14">k2</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="E19:6"/>
( <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">k1</font> &amp; <font color="Maroon" title="c12">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">k2</font> )
 
<b>by </b><i><a class="txt" href="topalg_4.html#E17:6"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="group_7.html#T2" title="GROUP_7:th.2">GROUP_7:2</a></i>;<br/>
<b>hence </b><a NAME="E20:6"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</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>
 <b>by </b><i><a class="txt" href="topalg_4.html#E6:6"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="topalg_4.html#E9:6"><i><font color="Green" title="E11">A5</font></i></a>, <a class="txt" href="topalg_4.html#E12:6"><i><font color="Green" title="E13">A7</font></i></a>, <a class="txt" href="topalg_4.html#E15:6"><i><font color="Green" title="E15">A9</font></i></a>, <a class="txt" href="topalg_4.html#E18:6"><i><font color="Green" title="E17">A11</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>


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