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<b>let </b><font color="Maroon">c<sub>7</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="analmetr.html#L1" target="_self">ParOrtStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>7</sub></font>;<br/>









<div><i><font color="Green">E61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>14</sub></font>
 ;<br/><a NAME="E2:75_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D14" target="_self">Def14</a></i>;<br/><b>hence </b><a NAME="E3:75_1"/>
<font color="Maroon">c<sub>14</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i><a class="ref" href="analmetr.html#D13" target="_self">Def13</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:75_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R7" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E2:75_2"/><b>then </b><i><font color="Green">E62</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>7</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="analmetr.html#K4" target="_self">Line</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>by </b><i><a class="ref" href="analmetr.html#D15" target="_self">Def15</a></i>;<br/><b>hence </b><a NAME="E3:75_2"/>
<font color="Maroon">c<sub>10</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i><a class="ref" href="analmetr.html#D13" target="_self">Def13</a></i>;<br/><b>thus </b><a NAME="E4:75_2"/>
<font color="Maroon">c<sub>11</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a>
 <b>by </b><i><a class="txt" href="analmetr.html#E1:75"><i><font color="Green">E61</font></i></a>, <a class="txt" href="analmetr.html#E2:75_2"><i><font color="Green">E62</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75"/>
( ( <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R6" target="_self">_|_</a> <font color="Maroon">c<sub>10</sub></font> implies <font color="Maroon">c<sub>10</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a> ) &amp; ( <font color="Maroon">c<sub>10</sub></font> <a href="analmetr.html#R7" target="_self">_|_</a> <font color="Maroon">c<sub>11</sub></font> implies ( <font color="Maroon">c<sub>10</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a> &amp; <font color="Maroon">c<sub>11</sub></font> is <a href="analmetr.html#V4" target="_self">being_line</a> ) ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E1:75"><i><font color="Green">E61</font></i></a></i>;<br/>


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