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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>set </b><font color="Maroon" title="c2">G</font> =  <a href="aofa_000.html#K11" title="AOFA_000:func.11">Generators</a> <font color="Maroon" title="c1">A</font>;<br/>
<b>let </b><font color="Maroon" title="c3">o</font> be   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">A</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">o'</font> be   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c5">p</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/><b>reconsider </b><font color="Maroon" title="c6">op</font> =  <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c4">o'</font>,<font color="Maroon" title="c1">A</font> as    <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>assume </b><a NAME="E2:66_1"/>
<font color="Maroon" title="c5">p</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> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c4">o'</font>,<font color="Maroon" title="c1">A</font></span>)</span>
 ;<br/><a NAME="E3:66_1"/><b>then </b>
<font color="Maroon" title="c6">op</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">op</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/><b>hence </b><a NAME="E4:66_1"/>
( <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c4">o'</font>,<font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aofa_000.html#K11" title="AOFA_000:func.11">Generators</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c4">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">o</font> )
 <b>by </b><i><a class="ref" href="aofa_000.html#T26" target="_self" title="AOFA_000:th.26">Th26</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:66"/>
for <font color="Olive" title="b1">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p</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> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c1">A</font></span>)</span> holds <br/>for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K11" title="AOFA_000:func.11">Generators</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> holds <br/> <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K11" title="AOFA_000:func.11">Generators</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <font color="Olive" title="b2">n</font>
 <b>by </b><i><a class="ref" href="aofa_000.html#T39" target="_self" title="AOFA_000:th.39">Th39</a></i>;<br/>


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