<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">N</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b2">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Olive" title="b1">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b2">N</font></span>)</span>,<font color="Olive" title="b2">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>,<font color="Olive" title="b1">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Olive" title="b2">N</font></span>)</span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">N</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b1">N</font></span>)</span>,<font color="Olive" title="b1">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>,<font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>,<font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">g</font> = <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">I</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">J</font> = (<span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a> ;<br/>
<a NAME="E1:101"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> <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 <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#D5" onmouseover="rs('group_2/D5')" onmouseout="rh()">GROUP_2:def 5</a></span>;<br/>
<a NAME="E2:101"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</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 <font color="Maroon" title="c1">G</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="relat_1.html#T61" onmouseover="rs('relat_1/T61')" onmouseout="rh()">RELAT_1:61</a></span>;<br/>
<a NAME="E3:101"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</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 <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/>
<a NAME="E4:101"/><span class="lab"><font color="Green" title="E60">A4</font></span>: 
<font color="Maroon" title="c3">N</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T60" onmouseover="rs('group_4/T60')" onmouseout="rh()">GROUP_4:60</a></span>;<br/>
<a NAME="E5:101"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A5</font></span>: 
<font color="Maroon" title="c3">N</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D1" target="_self" onmouseover="rs('group_6/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E6:101"/><span class="lab"><font color="Green" title="E62">A6</font></span>: 
<font color="Maroon" title="c2">B</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T60" onmouseover="rs('group_4/T60')" onmouseout="rh()">GROUP_4:60</a></span>;<br/>
<a NAME="E7:101"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span> or <font color="Maroon" title="c8">y</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:101_1"/>
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">y</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:101_1"/><span class="lab"><font color="Green" title="E63">A7</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:101_1"/><span class="lab"><font color="Green" title="E64">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">x</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="txt" href="#E1:101"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E3:101_1"><span class="lab"><font color="Green" title="E63">A7</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">x9</font> = <font color="Maroon" title="c10">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">x99</font> = <font color="Maroon" title="c10">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:101"><span class="lab"><font color="Green" title="E62">A6</font></span></a>, <a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<a NAME="E8:101_1"/><span class="lab"><font color="Green" title="E65">A9</font></span>: 
( <font color="Maroon" title="c12">x99</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">x9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c3">N</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c11">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">x99</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:101"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="lab"><font color="Green" title="E66">A10</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1"><span class="lab"><font color="Green" title="E63">A7</font></span></a>, <a class="ref" href="funct_1.html#T47" onmouseover="rs('funct_1/T47')" onmouseout="rh()">FUNCT_1:47</a></span>
<br/>.= 
<font color="Maroon" title="c11">x9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>
;<br/>
<a NAME="E10:101_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c11">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T117" onmouseover="rs('group_3/T117')" onmouseout="rh()">GROUP_3:117</a></span>;<br/>
<a NAME="E11:101_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">y</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:101_1"><span class="lab"><font color="Green" title="E64">A8</font></span></a>, <a class="txt" href="#E9:101_1"><span class="lab"><font color="Green" title="E66">A10</font></span></a>, <a class="txt" href="#E8:101_1"><span class="lab"><font color="Green" title="E65">A9</font></span></a>, <a class="ref" href="group_6.html#T23" target="_self" onmouseover="rs('group_6/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:101_1"/>
<font color="Maroon" title="c8">y</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">g</font> = <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a></span>;<br/>
<a NAME="E9:101"/><span class="lab"><font color="Green" title="E63">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:101"><span class="lab"><font color="Green" title="E60">A4</font></span></a>, <a class="ref" href="group_6.html#T28" target="_self" onmouseover="rs('group_6/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font> holds  <font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c11">a9</font> = <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c12">b9</font> = <font color="Maroon" title="c10">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/><a NAME="E2:101_2"/><span class="lab"><font color="Green" title="E64">A12</font></span>: 
( <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>;<br/><a NAME="E3:101_2"/>
<font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T43" onmouseover="rs('group_2/T43')" onmouseout="rh()">GROUP_2:43</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c10">b</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</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="c11">a9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">a9</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D6" target="_self" onmouseover="rs('group_6/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:101"><span class="lab"><font color="Green" title="E63">A11</font></span></a>, <a class="txt" href="#E2:101_2"><span class="lab"><font color="Green" title="E64">A12</font></span></a>, <a class="ref" href="group_2.html#T43" onmouseover="rs('group_2/T43')" onmouseout="rh()">GROUP_2:43</a></span>
;<br/> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c8">g</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D6" target="_self" onmouseover="rs('group_6/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E12:101"/><span class="lab"><font color="Green" title="E64">A13</font></span>: 
 <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_2.html#D6" onmouseover="rs('group_2/D6')" onmouseout="rh()">GROUP_2:def 6</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  not <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font> or <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font> ) &amp; (  not <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font> ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">c</font> = <font color="Maroon" title="c10">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<span class="lab"><font color="Green" title="E65">A14</font></span>: <font color="Maroon" title="c9">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<font color="Maroon" title="c11">c</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E3:101_3"/>
( <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font> implies <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:101_3_2"/>
<font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font></span><br/>

<span class="kw">then </span><font color="Maroon" title="c9">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b</font> = 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T41" target="_self" onmouseover="rs('group_6/T41')" onmouseout="rh()">Th41</a></span>
<br/>.= 
 <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T24" target="_self" onmouseover="rs('group_6/T24')" onmouseout="rh()">Th24</a></span>
<br/>.= 
 <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:101"><span class="lab"><font color="Green" title="E60">A4</font></span></a>, <a class="ref" href="group_6.html#D1" target="_self" onmouseover="rs('group_6/D1')" onmouseout="rh()">Def1</a></span>
;<br/>
<a NAME="E3:101_3_2"/><span class="kw">then </span>
( <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">N</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101_3"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="ref" href="group_2.html#T113" onmouseover="rs('group_2/T113')" onmouseout="rh()">GROUP_2:113</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:101_3_2"/>
<font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T82" onmouseover="rs('group_2/T82')" onmouseout="rh()">GROUP_2:82</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E4:101_3"/>
<font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font></span><br/>

<a NAME="E5:101_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T82" onmouseover="rs('group_2/T82')" onmouseout="rh()">GROUP_2:82</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c11">c</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font> = 
 <a href="group_2.html#K8" title="GROUP_2:func.8">carr</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:101"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="ref" href="group_2.html#T113" onmouseover="rs('group_2/T113')" onmouseout="rh()">GROUP_2:113</a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T24" target="_self" onmouseover="rs('group_6/T24')" onmouseout="rh()">Th24</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:101_3"/>
<font color="Maroon" title="c10">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Maroon" title="c9">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:101_3"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="ref" href="group_6.html#T41" target="_self" onmouseover="rs('group_6/T41')" onmouseout="rh()">Th41</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E13:101"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">g</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c10">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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> or <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">g</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:101_4"/>
<font color="Maroon" title="c10">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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">g</font></span><br/>

<a NAME="E2:101_4"/><span class="kw">then </span>
<font color="Maroon" title="c10">x</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:101_4"/><span class="lab"><font color="Green" title="E65">A15</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:101_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c11">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T23" target="_self" onmouseover="rs('group_6/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E6:101_4"/>
( <font color="Maroon" title="c2">B</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c11">b</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_5.html#T8" onmouseover="rs('group_5/T8')" onmouseout="rh()">GROUP_5:8</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">a1</font>, <font color="Maroon" title="c13">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E8:101_4"/><span class="lab"><font color="Green" title="E66">A16</font></span>: 
<font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c13">a2</font>
 <span class="kw">and </span><br/><a NAME="E9:101_4"/><span class="lab"><font color="Green" title="E67">A17</font></span>: 
<font color="Maroon" title="c12">a1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c2">B</font>
 <span class="kw">and </span><br/><a NAME="E10:101_4"/><span class="lab"><font color="Green" title="E68">A18</font></span>: 
<font color="Maroon" title="c13">a2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_5.html#T5" onmouseover="rs('group_5/T5')" onmouseout="rh()">GROUP_5:5</a></span>;<br/>
<a NAME="E11:101_4"/><span class="lab"><font color="Green" title="E69">A19</font></span>: 
<font color="Maroon" title="c12">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:101_4"><span class="lab"><font color="Green" title="E67">A17</font></span></a></span>;<br/>
<font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c13">a2</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:101"><span class="lab"><font color="Green" title="E61">A5</font></span></a>, <a class="txt" href="#E4:101_4"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="txt" href="#E8:101_4"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>
<br/>.= 
<font color="Maroon" title="c12">a1</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">a2</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T105" onmouseover="rs('group_2/T105')" onmouseout="rh()">GROUP_2:105</a></span>
<br/>.= 
<font color="Maroon" title="c12">a1</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:101_4"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="ref" href="group_2.html#T113" onmouseover="rs('group_2/T113')" onmouseout="rh()">GROUP_2:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">a1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D8" target="_self" onmouseover="rs('group_6/D8')" onmouseout="rh()">Def8</a></span>
<br/>.= 
<font color="Maroon" title="c9">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">a1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:101_4"><span class="lab"><font color="Green" title="E69">A19</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:101_4"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101"><span class="lab"><font color="Green" title="E59">A3</font></span></a>, <a class="txt" href="#E11:101_4"><span class="lab"><font color="Green" title="E69">A19</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E14:101"/><span class="kw">then </span>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<span class="p3">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c9">g</font>
 
;<br/>
<a NAME="E15:101"/><span class="kw">then </span>
<font color="Maroon" title="c9">g</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> 
 
;<br/>
<a NAME="E16:101"/><span class="kw">then </span>
 <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T57" target="_self" onmouseover="rs('group_6/T57')" onmouseout="rh()">Th57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:101"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">N</font></span>)</span>,<font color="Maroon" title="c3">N</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>,<font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K2" title="GROUP_6:func.2">/\</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:101"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="group_6.html#E91"><span class="lab"><font color="Green" title="E56">Lm3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
