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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="freealg.html#V3" title="FREEALG:attr.3">free</a> <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon" title="c2">o1</font>, <font color="Maroon" title="c3">o2</font> be    <a href="unialg_2.html#M2" title="UNIALG_2:mode.2">Element</a> of  <a href="unialg_2.html#K1" title="UNIALG_2:func.1">Operations</a> <font color="Maroon" title="c1">A</font>;<br/>



<b>consider </b><font color="Maroon" title="c4">a1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:63"/><i><font color="Green" title="E37">A1</font></i>: 
( <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c2">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">a1</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">a2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:63"/><i><font color="Green" title="E38">A2</font></i>: 
( <font color="Maroon" title="c5">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">a2</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">a1</font> = <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c7">a2</font> = <font color="Maroon" title="c5">a2</font> as   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="txt" href="aofa_000.html#E2:63"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="aofa_000.html#E4:63"><i><font color="Green" title="E38">A2</font></i></a></i>;<br/>
<a NAME="E6:63"/><i><font color="Green" title="E39">A3</font></i>: 
( <font color="Maroon" title="c2">o1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">o2</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="txt" href="aofa_000.html#E2:63"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="aofa_000.html#E4:63"><i><font color="Green" title="E38">A2</font></i></a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">p1</font>, <font color="Maroon" title="c9">p2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E7:63"/>
( <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">o1</font> &amp; <font color="Maroon" title="c9">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">o2</font> &amp; <font color="Maroon" title="c2">o1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">p2</font> )
 ;<br/>

<b>hence </b><a NAME="E8:63"/>
( <font color="Maroon" title="c2">o1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">o2</font> &amp; <font color="Maroon" title="c8">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">p2</font> )
 <b>by </b><i><a class="txt" href="aofa_000.html#E6:63"><i><font color="Green" title="E39">A3</font></i></a>, <a class="ref" href="aofa_000.html#T36" target="_self" title="AOFA_000:th.36">Th36</a></i>;<br/>


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