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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="unialg_2.html#R2">is_closed_on</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>then </b><i><font color="Green">E7</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> = 
0 <a href="finseq_2.html#K4">-tuples_on</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="unialg_2.html#T2">UNIALG_2:2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T112">FINSEQ_2:112</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>

<br/>.= 
0 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_2.html#T112">FINSEQ_2:112</a></i>
;<br/>
<a NAME="E3:10"/>
<font color="Maroon">c<sub>3</sub></font> <a href="unialg_2.html#K2">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default">0 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="unialg_3.html#E1:10"><i><font color="Green">E6</font></i></a>, <a class="ref" href="unialg_2.html#D6">UNIALG_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E4:10"/>
<font color="Maroon">c<sub>3</sub></font> <a href="unialg_2.html#K2">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="unialg_3.html#E2:10"><i><font color="Green">E7</font></i></a>, <a class="ref" href="relat_1.html#T98">RELAT_1:98</a></i>;<br/>


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