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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="freealg.html#V3" title="FREEALG:attr.3">free</a>  <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o1</font>, <font color="Olive" title="b2">o2</font> being   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">A</font><br/>  for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b3">p1</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Olive" title="b1">o1</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <font color="Olive" title="b4">p2</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Olive" title="b2">o2</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Olive" title="b1">o1</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="b3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Olive" title="b2">o2</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="b4">p2</font> holds <br/><font color="Olive" title="b1">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">o2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">G</font> =  the   <a href="freealg.html#V2" title="FREEALG:attr.2">free</a>   <a href="freealg.html#M1" title="FREEALG:mode.1">GeneratorSet</a> of <font color="Maroon" title="c1">A</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">o1</font>, <font color="Maroon" title="c4">o2</font> be   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p1</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <font color="Olive" title="b2">p2</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</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">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</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="b2">p2</font> holds <br/><font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c6">p2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p1</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <font color="Maroon" title="c6">p2</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</font>,<font color="Maroon" title="c1">A</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</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">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</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="c6">p2</font> implies <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:61"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c5">p1</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c1">A</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:61"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c6">p2</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"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</font>,<font color="Maroon" title="c1">A</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:61"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</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">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</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="c6">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">S</font> =  <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">A</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#T4" title="MSUALG_1:th.4">MSUALG_1:4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">B</font> being   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a><span class="kw"> such that </span><br/><a NAME="E6:61"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">and </span><br/><a NAME="E7:61"/><span class="lab"><font color="Green" title="E40">A5</font></span>: 
 <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c8">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">S</font>
 <span class="kw">and </span><br/><a NAME="E8:61"/><span class="lab"><font color="Green" title="E41">A6</font></span>: 
 for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</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> <font color="Maroon" title="c7">S</font> &amp; <font color="Olive" title="b2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">S</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">i</font> holds <br/> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">j</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Olive" title="b1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_000.html#T14" target="_self" title="AOFA_000:th.14">Th14</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">f</font> =  the   <a href="freealg.html#V2" title="FREEALG:attr.2">free</a>   <a href="freealg.html#M1" title="FREEALG:mode.1">GeneratorSet</a> of <font color="Maroon" title="c1">A</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the   <a href="freealg.html#V2" title="FREEALG:attr.2">free</a>   <a href="freealg.html#M1" title="FREEALG:mode.1">GeneratorSet</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">B</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E39">A4</font></span></a></span>;<br/>
<a NAME="E10:61"/>
<font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c8">B</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:61"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="unialg_2.html#D1" title="UNIALG_2:def.1">UNIALG_2:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">h</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c8">B</font><span class="kw"> such that </span><br/><a NAME="E12:61"/><span class="lab"><font color="Green" title="E42">A7</font></span>: 
<font color="Maroon" title="c10">h</font> <a href="alg_1.html#R1" title="ALG_1:pred.1">is_homomorphism</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c8">B</font>
 <span class="kw">and </span><br/><a NAME="E13:61"/>
<font color="Maroon" title="c10">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the   <a href="freealg.html#V2" title="FREEALG:attr.2">free</a>   <a href="freealg.html#M1" title="FREEALG:mode.1">GeneratorSet</a> of <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D5" title="FREEALG:def.5">FREEALG:def 5</a></span>;<br/>
<a NAME="E14:61"/><span class="lab"><font color="Green" title="E43">A8</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c8">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:61"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="unialg_1.html#D4" title="UNIALG_1:def.4">UNIALG_1:def 4</a></span>;<br/>
<a NAME="E15:61"/><span class="lab"><font color="Green" title="E44">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_1.html#D4" title="UNIALG_1:def.4">UNIALG_1:def 4</a></span>;<br/>
<a NAME="E16:61"/><span class="lab"><font color="Green" title="E45">A10</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c8">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E43">A8</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/>
<a NAME="E17:61"/><span class="lab"><font color="Green" title="E46">A11</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:61"><span class="lab"><font color="Green" title="E44">A9</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">b1</font> = <font color="Maroon" title="c3">o1</font>, <font color="Maroon" title="c12">b2</font> = <font color="Maroon" title="c4">o2</font> as   <a href="pua2mss1.html#NM2" title="PUA2MSS1:NM.2">OperSymbol</a> of <font color="Maroon" title="c8">B</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E43">A8</font></span></a>, <a class="txt" href="#E15:61"><span class="lab"><font color="Green" title="E44">A9</font></span></a>, <a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">n1</font> = <font color="Maroon" title="c3">o1</font>, <font color="Maroon" title="c14">n2</font> = <font color="Maroon" title="c4">o2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c15">j1</font> = <font color="Maroon" title="c7">S</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c13">n1</font>, <font color="Maroon" title="c16">j2</font> = <font color="Maroon" title="c7">S</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c14">n2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">x1</font> = <font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c18">x2</font> = <font color="Maroon" title="c6">p2</font> as   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c19">h1</font> = <font color="Maroon" title="c10">h</font> <a href="lang1.html#K11" title="LANG1:func.11">*</a> <font color="Maroon" title="c17">x1</font>, <font color="Maroon" title="c20">h2</font> = <font color="Maroon" title="c10">h</font> <a href="lang1.html#K11" title="LANG1:func.11">*</a> <font color="Maroon" title="c18">x2</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E39">A4</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c21">oo1</font> =  <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c1">A</font>), <font color="Maroon" title="c22">oo2</font> =  <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</font>,<font color="Maroon" title="c1">A</font>) as    <a href="margrel1.html#M5" title="MARGREL1:mode.5">Element</a> of  <a href="unialg_2.html#K1" title="UNIALG_2:func.1">Operations</a> <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E24:61"/><span class="lab"><font color="Green" title="E47">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c21">oo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c21">oo1</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T22" title="MARGREL1:th.22">MARGREL1:22</a></span>;<br/>
<a NAME="E25:61"/><span class="lab"><font color="Green" title="E48">A13</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c22">oo2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c22">oo2</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="margrel1.html#T22" title="MARGREL1:th.22">MARGREL1:22</a></span>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">x1</font> = 
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c21">oo1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E24:61"><span class="lab"><font color="Green" title="E47">A12</font></span></a>, <a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c15">j1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:61"><span class="lab"><font color="Green" title="E46">A11</font></span></a>, <a class="ref" href="unialg_1.html#D4" title="UNIALG_1:def.4">UNIALG_1:def 4</a></span>
;<br/>
<a NAME="E27:61"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c19">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">j1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T33" title="FINSEQ_2:th.33">FINSEQ_2:33</a></span>;<br/>
<a NAME="E28:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A14</font></span>: 
<font color="Maroon" title="c19">h1</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c15">j1</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T92" title="FINSEQ_2:th.92">FINSEQ_2:92</a></span>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c18">x2</font> = 
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c22">oo2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E25:61"><span class="lab"><font color="Green" title="E48">A13</font></span></a>, <a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>
<br/>.= 
<font color="Maroon" title="c16">j2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:61"><span class="lab"><font color="Green" title="E46">A11</font></span></a>, <a class="ref" href="unialg_1.html#D4" title="UNIALG_1:def.4">UNIALG_1:def 4</a></span>
;<br/>
<a NAME="E30:61"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c20">h2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">j2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T33" title="FINSEQ_2:th.33">FINSEQ_2:33</a></span>;<br/>
<a NAME="E31:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A15</font></span>: 
<font color="Maroon" title="c20">h2</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c16">j2</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T92" title="FINSEQ_2:th.92">FINSEQ_2:92</a></span>;<br/>
<a NAME="E32:61"/><span class="lab"><font color="Green" title="E51">A16</font></span>: 
 <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</font>,<font color="Maroon" title="c1">A</font>) is    <a href="margrel1.html#M5" title="MARGREL1:mode.5">Element</a> of  <a href="unialg_2.html#K1" title="UNIALG_2:func.1">Operations</a> <font color="Maroon" title="c1">A</font>
 
;<br/>
<a NAME="E33:61"/><span class="lab"><font color="Green" title="E52">A17</font></span>: 
 <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c8">B</font>) is    <a href="margrel1.html#M5" title="MARGREL1:mode.5">Element</a> of  <a href="unialg_2.html#K1" title="UNIALG_2:func.1">Operations</a> <font color="Maroon" title="c8">B</font>
 
;<br/>
<a NAME="E34:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A18</font></span>: 
<font color="Maroon" title="c10">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c3">o1</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="c17">x1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c8">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">h1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="txt" href="#E32:61"><span class="lab"><font color="Green" title="E51">A16</font></span></a>, <a class="ref" href="alg_1.html#D1" title="ALG_1:def.1">ALG_1:def 1</a></span>;<br/>
<a NAME="E35:61"/><span class="lab"><font color="Green" title="E54">A19</font></span>: 
<font color="Maroon" title="c10">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c4">o2</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="c18">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c12">b2</font>,<font color="Maroon" title="c8">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">h2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E42">A7</font></span></a>, <a class="txt" href="#E32:61"><span class="lab"><font color="Green" title="E51">A16</font></span></a>, <a class="txt" href="#E33:61"><span class="lab"><font color="Green" title="E52">A17</font></span></a>, <a class="ref" href="alg_1.html#D1" title="ALG_1:def.1">ALG_1:def 1</a></span>;<br/>
<a NAME="E36:61"/><span class="lab"><font color="Green" title="E55">A20</font></span>: 
 <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c8">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">j1</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span>)</span> <a href="aofa_000.html#K1" title="AOFA_000:func.1">--&gt;</a> <font color="Maroon" title="c13">n1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="txt" href="#E16:61"><span class="lab"><font color="Green" title="E45">A10</font></span></a></span>;<br/>
<a NAME="E37:61"/><span class="lab"><font color="Green" title="E56">A21</font></span>: 
 <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c12">b2</font>,<font color="Maroon" title="c8">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">j2</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span>)</span> <a href="aofa_000.html#K1" title="AOFA_000:func.1">--&gt;</a> <font color="Maroon" title="c14">n2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="txt" href="#E16:61"><span class="lab"><font color="Green" title="E45">A10</font></span></a></span>;<br/>
<a NAME="E38:61"/>
<span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> (<font color="Maroon" title="c11">b1</font>,<font color="Maroon" title="c8">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">n1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:61"><span class="lab"><font color="Green" title="E49">A14</font></span></a>, <a class="txt" href="#E36:61"><span class="lab"><font color="Green" title="E55">A20</font></span></a>, <a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E39:61"/>
<font color="Maroon" title="c3">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">o2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E31:61"><span class="lab"><font color="Green" title="E50">A15</font></span></a>, <a class="txt" href="#E34:61"><span class="lab"><font color="Green" title="E53">A18</font></span></a>, <a class="txt" href="#E35:61"><span class="lab"><font color="Green" title="E54">A19</font></span></a>, <a class="txt" href="#E37:61"><span class="lab"><font color="Green" title="E56">A21</font></span></a>, <a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
