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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="prvect_1.html#NM1">Domain-Sequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="prvect_1.html#M1" target="_self">BinOps</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="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:49"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K4">product</a> <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:49_1"/><i><font color="Green">E31</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:49_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><a NAME="E3:49_1_1"/>
( <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:49"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prvect_1.html#D10" target="_self">Def10</a></i>;<br/><b>hence </b><a NAME="E4:49_1_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:49_1"/>
<span class="p1"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:49_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:49_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> ;<br/><a NAME="E3:49_1_2"/>
( <span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="prvect_1.html#K9" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>2</sub></font> <a href="prvect_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:49"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prvect_1.html#D10" target="_self">Def10</a></i>;<br/><b>hence </b><a NAME="E4:49_1_2"/>
<span class="p1">(<span class="default"><span class="p2"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:49_1"/>
<span class="p1"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span> <a href="prvect_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:49_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:49"/>
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <span class="p1"><a href="prvect_1.html#K14" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="prvect_1.html#K14" target="_self">:]</a></span>
 <b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/>


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