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<b>let </b><font color="Maroon">G1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">G2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">H1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">H2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G1</font>,<font color="Maroon">H1</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G2</font>,<font color="Maroon">H2</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E39</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E40</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a><br/>

<b>set </b><font color="Maroon">h</font> =  <a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>;<br/>
<b>thus </b><a NAME="E3:6"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2">product</a> <span class="p2"><a href="group_7.html#K11">&lt;*</a><span class="default"><font color="Maroon">H1</font>,<font color="Maroon">H2</font></span><a href="group_7.html#K11">*&gt;</a></span></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>,<a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a><br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:6"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2">product</a> <span class="p2"><a href="group_7.html#K11">&lt;*</a><span class="default"><font color="Maroon">H1</font>,<font color="Maroon">H2</font></span><a href="group_7.html#K11">*&gt;</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H1</font>, <font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H2</font><b> such that </b><br/><a NAME="E6:6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">a1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:6"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E9:6"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">a2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:6"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E12:6"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E13:6"/><i><font color="Green">E63</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2">product</a> <span class="p2"><a href="group_7.html#K11">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="group_7.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E14:6"/>
for <font color="Olive">g</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font><br/> for <font color="Olive">h</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font> holds  <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Olive">g</font>,<font color="Olive">h</font></span><a href="group_7.html#K17">*&gt;</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2">product</a> <span class="p2"><a href="group_7.html#K11">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="group_7.html#K11">*&gt;</a></span></span>)</span>
 
;<br/>
<a NAME="E15:6"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<b>then consider </b><font color="Maroon">k1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>, <font color="Maroon">k2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font><b> such that </b><br/><a NAME="E17:6"/><i><font color="Green">E76</font></i>: 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Maroon">k1</font>,<font color="Maroon">k2</font></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:6"/><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">k2</font></span>)</span></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>by </b><i/>;<br/>
<a NAME="E19:6"/>
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k1</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font> )
 
<b>by </b><i>, <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/>
<b>hence </b><a NAME="E20:6"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K1" target="_self">Gr2Iso</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span>
 <b>by </b><i>, , , , , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


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