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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>, <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A1</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b2">A2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b3">A3</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X3</font><br/>  for <font color="Olive" title="b4">A4</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">X4</font><br/>  for <font color="Olive" title="b5">A5</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font><br/>  for <font color="Olive" title="b6">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b7">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b8">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Olive" title="b1">A1</font>,<font color="Olive" title="b2">A2</font>,<font color="Olive" title="b3">A3</font>,<font color="Olive" title="b4">A4</font>,<font color="Olive" title="b5">A5</font>,<font color="Olive" title="b6">A6</font>,<font color="Olive" title="b7">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A1</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A2</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A3</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">A4</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">A5</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b6">A6</font> &amp; <font color="Olive" title="b8">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">A1</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X1</font>; <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">A2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b2">A3</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X3</font><br/>  for <font color="Olive" title="b3">A4</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">X4</font><br/>  for <font color="Olive" title="b4">A5</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font><br/>  for <font color="Olive" title="b5">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b6">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b7">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Olive" title="b1">A2</font>,<font color="Olive" title="b2">A3</font>,<font color="Olive" title="b3">A4</font>,<font color="Olive" title="b4">A5</font>,<font color="Olive" title="b5">A6</font>,<font color="Olive" title="b6">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A2</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A3</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A4</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">A5</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">A6</font> &amp; <font color="Olive" title="b7">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b6">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">A2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X2</font>; <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">A3</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X3</font><br/>  for <font color="Olive" title="b2">A4</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">X4</font><br/>  for <font color="Olive" title="b3">A5</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font><br/>  for <font color="Olive" title="b4">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b5">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b6">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Olive" title="b1">A3</font>,<font color="Olive" title="b2">A4</font>,<font color="Olive" title="b3">A5</font>,<font color="Olive" title="b4">A6</font>,<font color="Olive" title="b5">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A3</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A4</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A5</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">A6</font> &amp; <font color="Olive" title="b6">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c10">A3</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">X3</font>; <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">A4</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">X4</font><br/>  for <font color="Olive" title="b2">A5</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font><br/>  for <font color="Olive" title="b3">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b4">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b5">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Olive" title="b1">A4</font>,<font color="Olive" title="b2">A5</font>,<font color="Olive" title="b3">A6</font>,<font color="Olive" title="b4">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A4</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A5</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A6</font> &amp; <font color="Olive" title="b5">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">A4</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">X4</font>; <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">A5</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font><br/>  for <font color="Olive" title="b2">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b3">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b4">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Olive" title="b1">A5</font>,<font color="Olive" title="b2">A6</font>,<font color="Olive" title="b3">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A5</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A6</font> &amp; <font color="Olive" title="b4">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c12">A5</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c5">X5</font>; <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">A6</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font><br/>  for <font color="Olive" title="b2">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b3">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Olive" title="b1">A6</font>,<font color="Olive" title="b2">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A6</font> &amp; <font color="Olive" title="b3">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c13">A6</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c6">X6</font>; <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">A7</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font><br/>  for <font color="Olive" title="b2">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Maroon" title="c13">A6</font>,<font color="Olive" title="b1">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font> &amp; <font color="Olive" title="b2">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c14">A7</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">X7</font>; <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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</a></span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Maroon" title="c13">A6</font>,<font color="Maroon" title="c14">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> holds <br/>( <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font> &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A7</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c15">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#K18" title="MCART_2:func.18">[:</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_2.html#K18" title="MCART_2:func.18">:]</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="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Maroon" title="c13">A6</font>,<font color="Maroon" title="c14">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> implies ( <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A7</font> ) )</span><br/>





























<span class="kw">assume </span><a NAME="E1:104"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Maroon" title="c13">A6</font>,<font color="Maroon" title="c14">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</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="c15">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A7</font> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">y</font> = <font color="Maroon" title="c15">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c8">A1</font>,<font color="Maroon" title="c9">A2</font>,<font color="Maroon" title="c10">A3</font>,<font color="Maroon" title="c11">A4</font>,<font color="Maroon" title="c12">A5</font>,<font color="Maroon" title="c13">A6</font>,<font color="Maroon" title="c14">A7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> ;<br/>
<a NAME="E3:104"/>
<font color="Maroon" title="c9">A2</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E4:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A2</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font>
 
;<br/>
<a NAME="E5:104"/>
<font color="Maroon" title="c14">A7</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E6:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A7</font>
 
;<br/>
<a NAME="E7:104"/>
<font color="Maroon" title="c11">A4</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E8:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A4</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font>
 
;<br/>
<a NAME="E9:104"/>
<font color="Maroon" title="c10">A3</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E10:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A5</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font>
 
;<br/>
<a NAME="E11:104"/>
<font color="Maroon" title="c13">A6</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E12:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A6</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font>
 
;<br/>
<a NAME="E13:104"/>
<font color="Maroon" title="c12">A5</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E14:104"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A7</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font>
 
;<br/>
<a NAME="E15:104"/>
<font color="Maroon" title="c8">A1</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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:104"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<a NAME="E16:104"/><span class="kw">then </span>
<font color="Maroon" title="c16">y</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E17:104"/>
( <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K19" title="MCART_2:func.19">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">A1</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K20" title="MCART_2:func.20">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">A2</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K21" title="MCART_2:func.21">`3</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">A3</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K22" title="MCART_2:func.22">`4</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">A4</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K23" title="MCART_2:func.23">`5</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">A5</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K24" title="MCART_2:func.24">`6</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">A6</font> &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_2.html#K25" title="MCART_2:func.25">`7</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">A7</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:104"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E10:104"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="txt" href="#E8:104"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="txt" href="#E14:104"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="txt" href="#E12:104"><span class="lab"><font color="Green" title="E77">A6</font></span></a>, <a class="txt" href="#E6:104"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="mcart_2.html#T110" target="_self" title="MCART_2:th.110">Th112</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/>


</div>
