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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>, <font color="Maroon" title="c8">Y1</font>, <font color="Maroon" title="c9">Y2</font>, <font color="Maroon" title="c10">Y3</font>, <font color="Maroon" title="c11">Y4</font>, <font color="Maroon" title="c12">Y5</font>, <font color="Maroon" title="c13">Y6</font>, <font color="Maroon" title="c14">Y7</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>  &amp; <font color="Maroon" title="c8">Y1</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="c9">Y2</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="c10">Y3</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="c11">Y4</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="c12">Y5</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="c13">Y6</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="c14">Y7</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><br/> for <font color="Olive" title="b2">y</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="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  ) )</span><br/>



























<b>assume </b><b>that </b><br/><a NAME="E1:71"/><i><font color="Green" title="E50">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>  )
 <b>and </b><br/><a NAME="E2:71"/><i><font color="Green" title="E51">A2</font></i>: 
( <font color="Maroon" title="c8">Y1</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="c9">Y2</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="c10">Y3</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="c11">Y4</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="c12">Y5</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="c13">Y6</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="c14">Y7</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><br/> for <font color="Olive" title="b2">y</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="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>let </b><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_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"> for <font color="Olive" title="b1">y</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="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>  st <font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> holds <br/>( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/><b>let </b><font color="Maroon" title="c16">y</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="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</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="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> implies ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  ) )</span><br/>



<b>assume </b><a NAME="E3:71"/><i><font color="Green" title="E52">A3</font></i>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K11" title="MCART_3:func.11">`1</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K12" title="MCART_3:func.12">`2</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K13" title="MCART_3:func.13">`3</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K14" title="MCART_3:func.14">`4</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K15" title="MCART_3:func.15">`5</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  &amp; <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K16" title="MCART_3:func.16">`6</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> </span><br/>

<b>thus </b><font color="Maroon" title="c15">x</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a>  = 
<font color="Maroon" title="c15">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</a></i>
<br/>.= 
<font color="Maroon" title="c16">y</font> <a href="mcart_3.html#K17" title="MCART_3:func.17">`7</a> 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E51">A2</font></i></a>, <a class="txt" href="#E3:71"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="mcart_3.html#T59" target="_self" title="MCART_3:th.59">Th59</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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