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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<a NAME="E1:147"/>
<font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c2">X</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a> <font color="Maroon" title="c2">X</font>)
 
<b>by </b><i><a class="ref" href="monoid_0.html#T25" target="_self" title="MONOID_0:th.25">Th25</a></i>;<br/>
<a NAME="E2:147"/><b>then </b>
( <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a> <font color="Maroon" title="c2">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c2">X</font> &amp; ( <font color="Maroon" title="c1">x</font> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c2">X</font> ) &amp; ( <font color="Maroon" title="c1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c2">X</font></span>)</span> implies <font color="Maroon" title="c1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K15" title="MONOID_0:func.15">GFuncs</a> <font color="Maroon" title="c2">X</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D40" target="_self" title="MONOID_0:def.40">Def40</a>, <a class="ref" href="funct_2.html#T12" title="FUNCT_2:th.12">FUNCT_2:12</a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:147"/>
( <font color="Maroon" title="c1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_0.html#K17" title="MONOID_0:func.17">GPerms</a> <font color="Maroon" title="c2">X</font></span>)</span> iff <font color="Maroon" title="c1">x</font> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Maroon" title="c2">X</font> )
 <b>by </b><i><a class="ref" href="monoid_0.html#D42" target="_self" title="MONOID_0:def.42">Def42</a></i>;<br/>


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