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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c7">X7</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</font>,<font color="Maroon" title="c5">X5</font>,<font color="Maroon" title="c6">X6</font>,<font color="Maroon" title="c7">X7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> holds  <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> </span>)</span></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span> )</span><br/>













<b>assume </b><a NAME="E1:56"/><i><font color="Green" title="E43">A1</font></i>: 
( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</font>,<font color="Maroon" title="c5">X5</font>,<font color="Maroon" title="c6">X6</font>,<font color="Maroon" title="c7">X7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> holds  <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> </span>)</span></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span></span><br/>

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</font>,<font color="Maroon" title="c5">X5</font>,<font color="Maroon" title="c6">X6</font>,<font color="Maroon" title="c7">X7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> </span>)</span></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span></span><br/>

<b>consider </b><font color="Maroon" title="c9">xx1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c10">xx2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c11">xx3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c12">xx4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c13">xx5</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c14">xx6</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c15">xx7</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X7</font><b> such that </b><br/><a NAME="E3:56"/><i><font color="Green" title="E44">A2</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><font color="Maroon" title="c9">xx1</font>,<font color="Maroon" title="c10">xx2</font>,<font color="Maroon" title="c11">xx3</font>,<font color="Maroon" title="c12">xx4</font>,<font color="Maroon" title="c13">xx5</font>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
 <b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="mcart_3.html#T56" target="_self" title="MCART_3:th.56">MC356</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c8">x</font> = 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<font color="Maroon" title="c10">xx2</font>,<font color="Maroon" title="c11">xx3</font>,<font color="Maroon" title="c12">xx4</font>,<font color="Maroon" title="c13">xx5</font>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D11" target="_self" title="MCART_3:def.11">Def11</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<font color="Maroon" title="c11">xx3</font>,<font color="Maroon" title="c12">xx4</font>,<font color="Maroon" title="c13">xx5</font>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D12" target="_self" title="MCART_3:def.12">Def12</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<font color="Maroon" title="c12">xx4</font>,<font color="Maroon" title="c13">xx5</font>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D13" target="_self" title="MCART_3:def.13">Def13</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<font color="Maroon" title="c13">xx5</font>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D14" target="_self" title="MCART_3:def.14">Def14</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<font color="Maroon" title="c14">xx6</font>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D15" target="_self" title="MCART_3:def.15">Def15</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> </span>)</span>,<font color="Maroon" title="c15">xx7</font></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D16" target="_self" title="MCART_3:def.16">Def16</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K9" title="MCART_3:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> </span>)</span></span><a href="mcart_3.html#K9" title="MCART_3:func.9">]</a></span>
<b>by </b><i><a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E3:56"><i><font color="Green" title="E44">A2</font></i></a>, <a class="ref" href="mcart_3.html#D17" target="_self" title="MCART_3:def.17">Def17</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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