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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="realset1.html#V1">trivial</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="realset1.html#K5">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>take </b>
 <a href="vectsp_1.html#G3">doubleLoopStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> #)
;<br/>

<b>thus </b><a NAME="E3:10_1_1"/>
( not  <a href="vectsp_1.html#G3">doubleLoopStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) is <a href="realset2.html#V3" target="_self">trivial</a> &amp;  <a href="vectsp_1.html#G3">doubleLoopStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> #) is <a href="vectsp_1.html#V3">strict</a> )
 <b>by </b><i><a class="txt" href="realset2.html#E8"><i><font color="Green">Lemma7</font></i></a></i>;<br/>


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