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<b>let </b><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">H</font> be   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>;<br/><b>let </b><font color="Maroon" title="c4">G'</font> be  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="group_9.html#NM4" title="GROUP_9:NM.4">Homomorphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c3">H</font>;<br/>







<b>reconsider </b><font color="Maroon" title="c6">G''</font> =  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">G'</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c4">G'</font> #) as  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G</font> <b>by </b><i><a class="txt" href="group_9.html#E40"><i><font color="Green" title="E38">Lm16</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">A</font> = <span class="p1">{<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="Olive" title="b1">g</font></span>)</span> where <font color="Olive" title="b1">g</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Olive" title="b1">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> </span>}</span> ;<br/>
<a NAME="E2:60"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T55" title="GROUP_2:th.55">GROUP_2:55</a></i>;<br/>
<a NAME="E3:60"/><b>then </b>
<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"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<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="Olive" title="b1">g</font></span>)</span> where <font color="Olive" title="b1">g</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Olive" title="b1">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">A</font> = <span class="p1">{<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="Olive" title="b1">g</font></span>)</span> where <font color="Olive" title="b1">g</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <font color="Olive" title="b1">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:60_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c10">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E3:60_1"/><i><font color="Green" title="E40">A1</font></i>: 
( <font color="Maroon" title="c9">x</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="c10">g</font> &amp; <font color="Maroon" title="c10">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 ;<br/><b>thus </b><a NAME="E4:60_1"/>
<font color="Maroon" title="c9">x</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 <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_1"><i><font color="Green" title="E40">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c9">A</font> = <font color="Maroon" title="c8">A</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c3">H</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<div><i><font color="Green" title="E40">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">h1</font>, <font color="Maroon" title="c11">h2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font>;<br/><b>assume </b><a NAME="E1:60_2"/><i><font color="Green" title="E41">A3</font></i>: 
( <font color="Maroon" title="c10">h1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> &amp; <font color="Maroon" title="c11">h2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c12">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E3:60_2"/><i><font color="Green" title="E42">A4</font></i>: 
( <font color="Maroon" title="c10">h1</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">a</font> &amp; <font color="Maroon" title="c12">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c13">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E5:60_2"/><i><font color="Green" title="E43">A5</font></i>: 
( <font color="Maroon" title="c11">h2</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="c13">b</font> &amp; <font color="Maroon" title="c13">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 <b>by </b><i><a class="txt" href="group_9.html#E1:60_2"><i><font color="Green" title="E41">A3</font></i></a></i>;<br/><a NAME="E6:60_2"/><i><font color="Green" title="E44">A6</font></i>: 
<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="c12">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">h1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h2</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_2"><i><font color="Green" title="E42">A4</font></i></a>, <a class="txt" href="group_9.html#E5:60_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="group_6.html#D7" title="GROUP_6:def.7">GROUP_6:def 7</a></i>;<br/><a NAME="E7:60_2"/>
<font color="Maroon" title="c12">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c13">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_2"><i><font color="Green" title="E42">A4</font></i></a>, <a class="txt" href="group_9.html#E5:60_2"><i><font color="Green" title="E43">A5</font></i></a>, <a class="ref" href="group_2.html#T59" title="GROUP_2:th.59">GROUP_2:59</a></i>;<br/><b>hence </b><a NAME="E8:60_2"/>
<font color="Maroon" title="c10">h1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c11">h2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="group_9.html#E6:60_2"><i><font color="Green" title="E44">A6</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E41">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font>;<br/><b>assume </b><a NAME="E1:60_3"/>
<font color="Maroon" title="c10">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c11">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E3:60_3"/><i><font color="Green" title="E42">A8</font></i>: 
( <font color="Maroon" title="c10">h</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="c11">g</font> &amp; <font color="Maroon" title="c11">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 ;<br/><a NAME="E4:60_3"/><i><font color="Green" title="E43">A9</font></i>: 
<font color="Maroon" title="c11">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_3"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="group_2.html#T60" title="GROUP_2:th.60">GROUP_2:60</a></i>;<br/><a NAME="E5:60_3"/>
<font color="Maroon" title="c10">h</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <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> <span class="p1">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_3"><i><font color="Green" title="E42">A8</font></i></a>, <a class="txt" href="group_9.html#E37"><i><font color="Green" title="E35">Lm14</font></i></a></i>;<br/><b>hence </b><a NAME="E6:60_3"/>
<font color="Maroon" title="c10">h</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="group_9.html#E4:60_3"><i><font color="Green" title="E43">A9</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">o</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">O</font>;<br/><b>let </b><font color="Maroon" title="c11">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font>;<br/><b>assume </b><a NAME="E1:60_4"/>
<font color="Maroon" title="c11">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c12">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E3:60_4"/><i><font color="Green" title="E42">A10</font></i>: 
( <font color="Maroon" title="c11">h</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">g</font> &amp; <font color="Maroon" title="c12">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 ;<br/><a NAME="E4:60_4"/><i><font color="Green" title="E43">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">h</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_4"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="group_9.html#D18" target="_self" title="GROUP_9:def.18">Def18</a></i>;<br/><a NAME="E5:60_4"/>
<font color="Maroon" title="c12">g</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 <font color="Maroon" title="c6">G''</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_4"><i><font color="Green" title="E42">A10</font></i></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><a NAME="E6:60_4"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><a NAME="E7:60_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="txt" href="group_9.html#E25"><i><font color="Green" title="E24">Lm10</font></i></a></i>;<br/><a NAME="E8:60_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">g</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 <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><a NAME="E9:60_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><b>hence </b><a NAME="E10:60_4"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="group_9.html#K3" title="GROUP_9:func.3">^</a> <font color="Maroon" title="c10">o</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="group_9.html#E4:60_4"><i><font color="Green" title="E43">A11</font></i></a></i>;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c10">H''</font> being  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>  <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font><b> such that </b><br/><a NAME="E11:60"/><i><font color="Green" title="E42">A12</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c10">H''</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="group_9.html#E7:60"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="group_9.html#E8:60"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="group_9.html#E38"><i><font color="Green" title="E36">Lm15</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">H'</font> =  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c10">H''</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c10">H''</font> #) as  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c3">H</font> <b>by </b><i><a class="txt" href="group_9.html#E40"><i><font color="Green" title="E38">Lm16</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c10">H''</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font>;<br/><b>set </b><font color="Maroon" title="c13">R</font> = <font color="Maroon" title="c5">f</font>;<br/><b>reconsider </b><font color="Maroon" title="c14">R</font> = <font color="Maroon" title="c5">f</font> as    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H</font> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:60_5_1"/>
<font color="Maroon" title="c12">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c15">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E3:60_5_1"/><i><font color="Green" title="E43">A13</font></i>: 
( <font color="Maroon" title="c12">h</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="c15">g</font> &amp; <font color="Maroon" title="c15">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font> )
 ;<br/><a NAME="E4:60_5_1"/>
 <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="c2">G</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/><a NAME="E5:60_5_1"/><b>then </b><i><font color="Green" title="E44">A14</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">g</font>,<font color="Maroon" title="c12">h</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_5_1"><i><font color="Green" title="E43">A13</font></i></a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><a NAME="E6:60_5_1"/>
<font color="Maroon" title="c15">g</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 <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="txt" href="group_9.html#E3:60_5_1"><i><font color="Green" title="E43">A13</font></i></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><b>hence </b><a NAME="E7:60_5_1"/>
<font color="Maroon" title="c12">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="txt" href="group_9.html#E5:60_5_1"><i><font color="Green" title="E44">A14</font></i></a>, <a class="ref" href="relset_1.html#T52" title="RELSET_1:th.52">RELSET_1:52</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E3:60_5"/>
<font color="Maroon" title="c12">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">G'</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c15">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E5:60_5"/><i><font color="Green" title="E43">A15</font></i>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">g</font>,<font color="Maroon" title="c12">h</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">R</font> &amp; <font color="Maroon" title="c15">g</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 <font color="Maroon" title="c4">G'</font> )
 <b>by </b><i><a class="ref" href="relset_1.html#T52" title="RELSET_1:th.52">RELSET_1:52</a></i>;<br/><a NAME="E6:60_5"/><i><font color="Green" title="E44">A16</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="c15">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">h</font>
 <b>by </b><i><a class="txt" href="group_9.html#E5:60_5"><i><font color="Green" title="E43">A15</font></i></a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/><a NAME="E7:60_5"/>
<font color="Maroon" title="c15">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c6">G''</font>
 <b>by </b><i><a class="txt" href="group_9.html#E5:60_5"><i><font color="Green" title="E43">A15</font></i></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/><b>hence </b><a NAME="E8:60_5"/>
<font color="Maroon" title="c12">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A</font>
 <b>by </b><i><a class="txt" href="group_9.html#E6:60_5"><i><font color="Green" title="E44">A16</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:60"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c10">H''</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="txt" href="group_9.html#E11:60"><i><font color="Green" title="E42">A12</font></i></a>, <a class="ref" href="subset_1.html#T8" title="SUBSET_1:th.8">SUBSET_1:8</a></i>;<br/>


</div>
