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<span class="kw">let </span><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <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">h</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>  st <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  holds <br/> for <font color="Olive" title="b2">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span><br/>  for <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b2">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9" title="MSUALG_1:func.9">MSAlg</a> <font color="Maroon" title="c1">U1</font></span>)</span>) holds  <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b3">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</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="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  implies  for <font color="Olive" title="b1">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span><br/>  for <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b1">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9" title="MSUALG_1:func.9">MSAlg</a> <font color="Maroon" title="c1">U1</font></span>)</span>) holds  <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">y</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</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">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span><br/>  for <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Olive" title="b1">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9" title="MSUALG_1:func.9">MSAlg</a> <font color="Maroon" title="c1">U1</font></span>)</span>) holds  <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b2">y</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">f1</font> = <span class="p1">(<span class="default"><a href="finseq_2.html#K7" title="FINSEQ_2:func.7">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#T2" title="MSUALG_1:th.2">MSUALG_1:2</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">o</font> be   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span>; <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">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9" title="MSUALG_1:func.9">MSAlg</a> <font color="Maroon" title="c1">U1</font></span>)</span>) holds  <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">y</font></span><br/>

<a NAME="E3:19"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c2">U2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D8" title="MSUALG_1:def.8">MSUALG_1:def 8</a></span>;<br/>
<a NAME="E4:19"/>
 <a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c2">U2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="msuhom_1.html#T10" target="_self" title="MSUHOM_1:th.10">Th10</a></span>;<br/>
<a NAME="E5:19"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</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> <span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:19"><span class="lab"><font color="Green" title="E18">A2</font></span></a></span>;<br/>
<a NAME="E6:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<font color="Maroon" title="c5">o</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> <span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="unialg_2.html#D1" title="UNIALG_2:def.1">UNIALG_2:def 1</a></span>;<br/>
<a NAME="E7:19"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</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> <font color="Maroon" title="c4">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E8:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K7" title="FINSEQ_2:func.7">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_2.html#K7" title="FINSEQ_2:func.7">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <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="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="msualg_1.html#K3" title="MSUALG_1:func.3">Args</a> (<font color="Maroon" title="c5">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9" title="MSUALG_1:func.9">MSAlg</a> <font color="Maroon" title="c1">U1</font></span>)</span>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">f</font> =  <a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font>;<br/>
<a NAME="E9:19"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D8" title="MSUALG_1:def.8">MSUALG_1:def 8</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">X</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font></span>)</span>;<br/>
<a NAME="E10:19"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">h</font> <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">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E11:19"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<font color="Maroon" title="c6">y</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msuhom_1.html#T14" target="_self" title="MSUHOM_1:th.14">Th14</a></span>;<br/>
<a NAME="E12:19"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">y</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">U1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E10:19"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="finseq_1.html#T16" title="FINSEQ_1:th.16">FINSEQ_1:16</a></span>;<br/>
<a NAME="E14:19"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="finseq_3.html#T120" title="FINSEQ_3:th.120">FINSEQ_3:120</a></span>;<br/>
<a NAME="E15:19"/>
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c4">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D8" title="MSUALG_1:def.8">MSUALG_1:def 8</a></span>;<br/>
<a NAME="E16:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A9</font></span>: 
 <a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_2.html#K7" title="FINSEQ_2:func.7">*--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D1" title="MSUALG_1:def.1">MSUALG_1:def 1</a></span>;<br/>
<a NAME="E17:19"/>
<span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</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"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:19"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">n</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E19:19"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
<font color="Maroon" title="c10">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">o</font>
 ;<br/>
<a NAME="E20:19"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E28">A12</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:19_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E2:19_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T63" title="FINSEQ_2:th.63">FINSEQ_2:63</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">l</font> = <font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K6" title="MSUALG_1:func.6">MSSign</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:19"><span class="lab"><font color="Green" title="E21">A5</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">let </span><font color="Maroon" title="c12">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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="c12">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font> implies <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> )</span><br/><a NAME="E4:19_1"/><span class="lab"><font color="Green" title="E29">A13</font></span>: 
( <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c10">n</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="finseq_2.html#D6" title="FINSEQ_2:def.6">FINSEQ_2:def 6</a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E5:19_1"/>
<font color="Maroon" title="c12">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font></span><br/><a NAME="E6:19_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">m</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> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T6" title="MSUALG_3:th.6">MSUALG_3:6</a></span>;<br/><a NAME="E7:19_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A14</font></span>: 
<font color="Maroon" title="c12">m</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> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="finseq_2.html#D6" title="FINSEQ_2:def.6">FINSEQ_2:def 6</a></span>;<br/><a NAME="E8:19_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">l</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/><a NAME="E9:19_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:19_1"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E4:19_1"><span class="lab"><font color="Green" title="E29">A13</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><span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">m</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="msuhom_1.html#D3" target="_self" title="MSUHOM_1:def.3">Def3</a>, <a class="ref" href="msuhom_1.html#T10" target="_self" title="MSUHOM_1:th.10">Th10</a></span>
<br/>.= 
<font color="Maroon" title="c3">h</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:19"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="funcop_1.html#T7" title="FUNCOP_1:th.7">FUNCOP_1:7</a></span>
;<br/> <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><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E29">A15</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font> )</span><br/><span class="kw">assume </span><a NAME="E1:19_2"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font></span><br/><a NAME="E2:19_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="finseq_3.html#T120" title="FINSEQ_3:th.120">FINSEQ_3:120</a></span>;<br/><a NAME="E3:19_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_2"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="msualg_3.html#D6" title="MSUALG_3:def.6">MSUALG_3:def 6</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font> = 
<font color="Maroon" title="c3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:19"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E1:19_2"><span class="lab"><font color="Green" title="E30">A16</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c9">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E2:19_2"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="finseq_3.html#T120" title="FINSEQ_3:th.120">FINSEQ_3:120</a></span>
;<br/> <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><span class="kw">end;</span></div>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T6" title="MSUALG_3:th.6">MSUALG_3:6</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="finseq_2.html#D6" title="FINSEQ_2:def.6">FINSEQ_2:def 6</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c10">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
;<br/>
<a NAME="E24:19"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A18</font></span>: 
<span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font> is   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D2" title="FINSEQ_1:def.2">FINSEQ_1:def 2</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A19</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">y</font> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T6" title="MSUALG_3:th.6">MSUALG_3:6</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="finseq_2.html#D6" title="FINSEQ_2:def.6">FINSEQ_2:def 6</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c10">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1" title="MSUALG_1:func.1">the_arity_of</a> <font color="Maroon" title="c5">o</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_3.html#T6" title="MSUALG_3:th.6">MSUALG_3:6</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">n</font> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:19"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E8:19"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E19:19"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="ref" href="finseq_2.html#D6" title="FINSEQ_2:def.6">FINSEQ_2:def 6</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c10">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:19"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E25:19"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="finseq_3.html#T120" title="FINSEQ_3:th.120">FINSEQ_3:120</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E27:19"/>
<span class="p1">(<span class="default"><a href="msuhom_1.html#K2" title="MSUHOM_1:func.2">MSAlg</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="msualg_3.html#K5" title="MSUALG_3:func.5">#</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:19"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E22:19"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E14:19"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="finseq_1.html#T13" title="FINSEQ_1:th.13">FINSEQ_1:13</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>
