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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:21"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="unialg_2.html#R1">are_similar</a> 
 ;<br/>

<a NAME="E2:21"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msuhom_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E3:21"/><i><font color="Green">E19</font></i>: 
0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7">MSUALG_1:7</a></i>;<br/>
<a NAME="E5:21"/><i><font color="Green">E20</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D13">MSUALG_1:def 13</a></i>;<br/>
<a NAME="E6:21"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_1.html#D6">MSUALG_1:def 6</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7">MSUALG_1:7</a></i>;<br/>
<a NAME="E8:21"/><i><font color="Green">E22</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D13">MSUALG_1:def 13</a></i>;<br/>
<a NAME="E9:21"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/>
<a NAME="E10:21"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E2:21"><i><font color="Green">E18</font></i></a>, <a class="txt" href="msuhom_1.html#E8:21"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E11:21"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E1:21"><i><font color="Green">E17</font></i></a>, <a class="ref" href="unialg_2.html#D2">UNIALG_2:def 2</a></i>;<br/>
<a NAME="E12:21"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E13:21"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E14:21"/>
<span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E11:21"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E16:21"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>
<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:21_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="msualg_3.html#T6">MSUALG_3:6</a></i>;<br/><a NAME="E3:21_1"/>
0 is    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:21_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0 is    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T77">FINSEQ_2:77</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0 as    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="txt" href="msuhom_1.html#E5:21"><i><font color="Green">E20</font></i></a>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/><a NAME="E6:21_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0</span>)</span>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="msuhom_1.html#E13:21"><i><font color="Green">E24</font></i></a>, <a class="txt" href="msuhom_1.html#E16:21"><i><font color="Green">E25</font></i></a>, <a class="txt" href="msuhom_1.html#E2:21_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="pboole.html#D20">PBOOLE:def 20</a></i>;<br/><a NAME="E7:21_1"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="msuhom_1.html#E13:21"><i><font color="Green">E24</font></i></a>, <a class="txt" href="msuhom_1.html#E16:21"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pboole.html#D20">PBOOLE:def 20</a></i>;<br/><a NAME="E8:21_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E6:21_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E9:21_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T68">FINSEQ_2:68</a></i>;<br/><a NAME="E10:21_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="msuhom_1.html#E6:21_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="msuhom_1.html#E7:21_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="msuhom_1.html#E8:21_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_2.html#T70">FINSEQ_2:70</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 0
<b>by </b><i><a class="txt" href="msuhom_1.html#E2:21"><i><font color="Green">E18</font></i></a>, <a class="ref" href="msuhom_1.html#D3" target="_self">Def3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="msuhom_1.html#E3:21"><i><font color="Green">E19</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E18:21"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="msuhom_1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E19:21"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<i><font color="Green">E29</font></i>:  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_3.html#T6">MSUALG_3:6</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="msuhom_1.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="msuhom_1.html#E13:21"><i><font color="Green">E24</font></i></a>, <a class="txt" href="msuhom_1.html#E16:21"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pboole.html#D20">PBOOLE:def 20</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T68">FINSEQ_2:68</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<i><font color="Green">E30</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_3.html#T6">MSUALG_3:6</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="msuhom_1.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="msuhom_1.html#E13:21"><i><font color="Green">E24</font></i></a>, <a class="txt" href="msuhom_1.html#E16:21"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pboole.html#D20">PBOOLE:def 20</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T68">FINSEQ_2:68</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="msuhom_1.html#E18:21"><i><font color="Green">E27</font></i></a>, <a class="txt" href="msuhom_1.html#E20:21"><i><font color="Green">E29</font></i></a>, <a class="ref" href="alg_1.html#T1">ALG_1:1</a></i>
;<br/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_3.html#T6">MSUALG_3:6</a></i>
<br/>.= 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="msuhom_1.html#K1" target="_self">|-&gt;</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="msuhom_1.html#E6:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="msuhom_1.html#E13:21"><i><font color="Green">E24</font></i></a>, <a class="txt" href="msuhom_1.html#E16:21"><i><font color="Green">E25</font></i></a>, <a class="ref" href="pboole.html#D20">PBOOLE:def 20</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T68">FINSEQ_2:68</a></i>
;<br/>
<a NAME="E23:21"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font> is   <a href="finseq_1.html#NM1">FinSequence</a>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E24:21"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="txt" href="msuhom_1.html#E18:21"><i><font color="Green">E27</font></i></a>, <a class="txt" href="msuhom_1.html#E19:21"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T20">FINSEQ_1:20</a></i>;<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="21_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:21_5"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:21_5"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E18:21"><i><font color="Green">E27</font></i></a>, <a class="ref" href="alg_1.html#T1">ALG_1:1</a></i>;<br/><a NAME="E3:21_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E1:21_5"><i><font color="Green">E33</font></i></a>, <a class="ref" href="msualg_3.html#D8">MSUALG_3:def 8</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="msuhom_1.html#E17:21"><i><font color="Green">E26</font></i></a>, <a class="txt" href="msuhom_1.html#E1:21_5"><i><font color="Green">E33</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="msuhom_1.html#E18:21"><i><font color="Green">E27</font></i></a>, <a class="txt" href="msuhom_1.html#E2:21_5"><i><font color="Green">E34</font></i></a>, <a class="ref" href="alg_1.html#T1">ALG_1:1</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E27:21"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="msuhom_1.html#E18:21"><i><font color="Green">E27</font></i></a>, <a class="ref" href="alg_1.html#T1">ALG_1:1</a></i>;<br/>
<b>hence </b><a NAME="E28:21"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="msuhom_1.html#E21:21"><i><font color="Green">E30</font></i></a>, <a class="txt" href="msuhom_1.html#E23:21"><i><font color="Green">E31</font></i></a>, <a class="txt" href="msuhom_1.html#E26:21"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


</div>
