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<b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM6">Function</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>,<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>, <font color="Maroon">G</font> be   <a href="struct_0.html#NM6">Function</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>,<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>assume </b><b>that </b><br/><a NAME="E1:2_1_2"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</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>  ex <font color="Olive">x1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font> ex <font color="Olive">x2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Olive">x1</font>,<font color="Olive">x2</font></span><a href="group_7.html#K17">*&gt;</a></span> &amp; <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <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="Olive">x1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x2</font></span>)</span></span><a href="group_7.html#K17">*&gt;</a></span> )
 <b>and </b><br/><a NAME="E2:2_1_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</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>  ex <font color="Olive">x1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font> ex <font color="Olive">x2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Olive">x1</font>,<font color="Olive">x2</font></span><a href="group_7.html#K17">*&gt;</a></span> &amp; <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <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="Olive">x1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x2</font></span>)</span></span><a href="group_7.html#K17">*&gt;</a></span> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</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/><b>consider </b><font color="Maroon">x1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>, <font color="Maroon">x2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font><b> such that </b><br/><a NAME="E2:2_1_2_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E3:2_1_2_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <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">x1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x2</font></span>)</span></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">y1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>, <font color="Maroon">y2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G2</font><b> such that </b><br/><a NAME="E5:2_1_2_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="group_7.html#K17">&lt;*</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>and </b><br/><a NAME="E6:2_1_2_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <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">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y2</font></span>)</span></span><a href="group_7.html#K17">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E7:2_1_2_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 <b>by </b><i>, , <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/><b>hence </b><a NAME="E8:2_1_2_1"/>
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:2_1_2"/>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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