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<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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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#K15" title="GROUP_7:func.15">&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#K15" title="GROUP_7:func.15">*&gt;</a></span></span>)</span>;<br/><b>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="E2:4_1_1_1"/><i><font color="Green" title="E5">A1</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="E3:4_1_1_1"/><i><font color="Green" title="E6">A2</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_2.html#K3" title="FUNCT_2:func.3">.</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>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="E5:4_1_1_1"/><i><font color="Green" title="E7">A3</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="E6:4_1_1_1"/><i><font color="Green" title="E8">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_2.html#K3" title="FUNCT_2:func.3">.</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/><b>consider </b><font color="Maroon" title="c14">r1</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="c15">r2</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="E8:4_1_1_1"/><i><font color="Green" title="E9">A5</font></i>: 
<font color="Maroon" title="c8">a</font> <a href="group_1.html#K1" title="GROUP_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"><font color="Maroon" title="c14">r1</font>,<font color="Maroon" title="c15">r2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E9:4_1_1_1"/><i><font color="Green" title="E10">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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">b</font></span>)</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="c14">r1</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="c15">r2</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="E10:4_1_1_1"/>
( <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&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#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <font color="Maroon" title="c8">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a1</font> &amp; <font color="Maroon" title="c9">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b1</font> )
 <b>by </b><i><a class="txt" href="topalg_4.html#E2:4_1_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="topalg_4.html#E5:4_1_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E11:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c10">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">b1</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="c14">r1</font>,<font color="Maroon" title="c15">r2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <b>by </b><i><a class="txt" href="topalg_4.html#E8:4_1_1_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="topalg_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="group_7.html#T4" title="GROUP_7:th.4">GROUP_7:4</a></i>;<br/><b>then </b><i><font color="Green" title="E11">A7</font></i>: <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">r1</font> = 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">a1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c12">b1</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<span class="p1">(<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> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a></i>
;<br/><a NAME="E13:4_1_1_1"/>
( <font color="Maroon" title="c2">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K15" title="GROUP_7:func.15">&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#K15" title="GROUP_7:func.15">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <font color="Maroon" title="c8">a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a2</font> &amp; <font color="Maroon" title="c9">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <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#E2:4_1_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="topalg_4.html#E5:4_1_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E14:4_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">a2</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c13">b2</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="c14">r1</font>,<font color="Maroon" title="c15">r2</font></span><a href="group_7.html#K17" title="GROUP_7:func.17">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
 <b>by </b><i><a class="txt" href="topalg_4.html#E8:4_1_1_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="topalg_4.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="group_7.html#T4" title="GROUP_7:th.4">GROUP_7:4</a></i>;<br/><b>then </b><font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">r2</font> = 
<font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">a2</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c13">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<span class="p1">(<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> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a></i>
;<br/><b>hence </b><a NAME="E16:4_1_1_1"/>
<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_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<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_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="topalg_4.html#E3:4_1_1_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="topalg_4.html#E6:4_1_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="topalg_4.html#E9:4_1_1_1"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="topalg_4.html#E12:4_1_1_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="group_7.html#T32" title="GROUP_7:th.32">GROUP_7:32</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:4_1_1"/>
 <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> is   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</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#K15" title="GROUP_7:func.15">&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#K15" title="GROUP_7:func.15">*&gt;</a></span></span>)</span>,<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#K15" title="GROUP_7:func.15">&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#K15" title="GROUP_7:func.15">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a></i>;<br/>


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