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<span class="kw">let </span><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> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>  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_2.html#K10" title="MCART_2: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></span><a href="mcart_2.html#K10" title="MCART_2: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_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a></span>)</span></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span> )</span><br/>











<span class="kw">assume </span><a NAME="E1:55"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
( <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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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_2.html#K10" title="MCART_2: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></span><a href="mcart_2.html#K10" title="MCART_2: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_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a></span>)</span></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_2.html#K10" title="MCART_2: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></span><a href="mcart_2.html#K10" title="MCART_2:func.10">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a></span>)</span></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">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="c9">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="c10">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="c11">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="c12">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="c13">xx6</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X6</font><span class="kw"> such that </span><br/><a NAME="E3:55"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><font color="Maroon" title="c8">xx1</font>,<font color="Maroon" title="c9">xx2</font>,<font color="Maroon" title="c10">xx3</font>,<font color="Maroon" title="c11">xx4</font>,<font color="Maroon" title="c12">xx5</font>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="mcart_2.html#T53" target="_self" title="MCART_2:th.53">Th55</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c7">x</font> = 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<font color="Maroon" title="c9">xx2</font>,<font color="Maroon" title="c10">xx3</font>,<font color="Maroon" title="c11">xx4</font>,<font color="Maroon" title="c12">xx5</font>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D10" target="_self" title="MCART_2:def.10">Def10</a></span>
<br/>.= 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<font color="Maroon" title="c10">xx3</font>,<font color="Maroon" title="c11">xx4</font>,<font color="Maroon" title="c12">xx5</font>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D11" target="_self" title="MCART_2:def.11">Def11</a></span>
<br/>.= 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<font color="Maroon" title="c11">xx4</font>,<font color="Maroon" title="c12">xx5</font>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D12" target="_self" title="MCART_2:def.12">Def12</a></span>
<br/>.= 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<font color="Maroon" title="c12">xx5</font>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D13" target="_self" title="MCART_2:def.13">Def13</a></span>
<br/>.= 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a></span>)</span>,<font color="Maroon" title="c13">xx6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D14" target="_self" title="MCART_2:def.14">Def14</a></span>
<br/>.= 
<span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a></span>)</span></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="mcart_2.html#D15" target="_self" title="MCART_2:def.15">Def15</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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