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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">Y1</font>, <font color="Maroon" title="c8">Y2</font>, <font color="Maroon" title="c9">Y3</font>, <font color="Maroon" title="c10">Y4</font>, <font color="Maroon" title="c11">Y5</font>, <font color="Maroon" title="c12">Y6</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="Red">::  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>  &amp; <font color="Maroon" title="c7">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="c8">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="c9">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="c10">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="c11">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="c12">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>  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><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_2.html#K10" title="MCART_2:func.10">[:</a><span class="default"><font color="Maroon" title="c7">Y1</font>,<font color="Maroon" title="c8">Y2</font>,<font color="Maroon" title="c9">Y3</font>,<font color="Maroon" title="c10">Y4</font>,<font color="Maroon" title="c11">Y5</font>,<font color="Maroon" title="c12">Y6</font></span><a href="mcart_2.html#K10" title="MCART_2: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_2.html#K11" title="MCART_2:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  ) )</span><br/>























<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:71"/><span class="lab"><font color="Green" title="E48">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>  )
 <span class="kw">and </span><br/><a NAME="E2:71"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
( <font color="Maroon" title="c7">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="c8">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="c9">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="c10">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="c11">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="c12">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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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><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_2.html#K10" title="MCART_2:func.10">[:</a><span class="default"><font color="Maroon" title="c7">Y1</font>,<font color="Maroon" title="c8">Y2</font>,<font color="Maroon" title="c9">Y3</font>,<font color="Maroon" title="c10">Y4</font>,<font color="Maroon" title="c11">Y5</font>,<font color="Maroon" title="c12">Y6</font></span><a href="mcart_2.html#K10" title="MCART_2: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_2.html#K11" title="MCART_2:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c13">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="Red">::  thesis: </font></span></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_2.html#K10" title="MCART_2:func.10">[:</a><span class="default"><font color="Maroon" title="c7">Y1</font>,<font color="Maroon" title="c8">Y2</font>,<font color="Maroon" title="c9">Y3</font>,<font color="Maroon" title="c10">Y4</font>,<font color="Maroon" title="c11">Y5</font>,<font color="Maroon" title="c12">Y6</font></span><a href="mcart_2.html#K10" title="MCART_2:func.10">:]</a></span>  st <font color="Maroon" title="c13">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="c13">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c14">y</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="c7">Y1</font>,<font color="Maroon" title="c8">Y2</font>,<font color="Maroon" title="c9">Y3</font>,<font color="Maroon" title="c10">Y4</font>,<font color="Maroon" title="c11">Y5</font>,<font color="Maroon" title="c12">Y6</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> implies ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E3:71"/><span class="lab"><font color="Green" title="E50">A3</font></span>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K11" title="MCART_2: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"><font color="Maroon" title="c13">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K11" title="MCART_2:func.11">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K12" title="MCART_2: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"><font color="Maroon" title="c13">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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K12" title="MCART_2:func.12">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K13" title="MCART_2:func.13">`3</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K14" title="MCART_2:func.14">`4</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  &amp; <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K15" title="MCART_2:func.15">`5</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a> </span><br/>

<span class="kw">thus </span><font color="Maroon" title="c13">x</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a>  = 
<font color="Maroon" title="c13">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
<br/>.= 
<font color="Maroon" title="c14">y</font> <a href="mcart_2.html#K16" title="MCART_2:func.16">`6</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:71"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E3:71"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="mcart_2.html#T58" target="_self" title="MCART_2:th.58">Th58</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
