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<div class="add">

<b>let </b><font color="Maroon" title="c3">r1</font>, <font color="Maroon" title="c4">r2</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>thus </b><a NAME="E1:33_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 &amp;  ex <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> ex <font color="Olive" title="b4">y</font>, <font color="Olive" title="b5">z</font> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b5">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b4">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b5">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">y</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="prelamb.html#K8" title="PRELAMB:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span></span>)</span></span>)</span> ) &amp;  ex <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> ex <font color="Olive" title="b4">y</font>, <font color="Olive" title="b5">z</font> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b5">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b4">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b5">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">y</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="prelamb.html#K8" title="PRELAMB:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span></span>)</span></span>)</span> ) implies <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:33_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/>

<b>given </b><font color="Maroon" title="c5">T</font>, <font color="Maroon" title="c6">X</font>, <font color="Maroon" title="c7">Y</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font>, <font color="Maroon" title="c8">y</font>, <font color="Maroon" title="c9">z</font> being   <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font><b> such that </b><a NAME="E3:33_1_2_1"/><i><font color="Green" title="E10">A4</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font></span>)</span>,<font color="Maroon" title="c9">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c8">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font></span>)</span>,<font color="Maroon" title="c9">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">y</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="prelamb.html#K8" title="PRELAMB:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon" title="c10">T'</font>, <font color="Maroon" title="c11">X'</font>, <font color="Maroon" title="c12">Y'</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font>, <font color="Maroon" title="c13">y'</font>, <font color="Maroon" title="c14">z'</font> being   <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font><b> such that </b><a NAME="E5:33_1_2_1"/><i><font color="Green" title="E11">A5</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">X'</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">T'</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c12">Y'</font></span>)</span>,<font color="Maroon" title="c14">z'</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Maroon" title="c10">T'</font>,<font color="Maroon" title="c13">y'</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">X'</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c13">y'</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c12">Y'</font></span>)</span>,<font color="Maroon" title="c14">z'</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">y'</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">z'</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prelamb.html#K7" title="PRELAMB:func.7">size_w.r.t.</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="prelamb.html#K8" title="PRELAMB:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">X'</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">T'</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c12">Y'</font></span>)</span></span>)</span></span>)</span> )
 ;<br/>

<i><font color="Green" title="E12">A6</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font> = 
<span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font></span>)</span>,<font color="Maroon" title="c9">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">X'</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c10">T'</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c12">Y'</font>
<b>by </b><i><a class="txt" href="prelamb.html#E3:33_1_2_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="prelamb.html#E5:33_1_2_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<i><font color="Green" title="E13">A7</font></i>: <font color="Maroon" title="c8">y</font> = 
<span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c8">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon" title="c13">y'</font>
<b>by </b><i><a class="txt" href="prelamb.html#E3:33_1_2_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="prelamb.html#E5:33_1_2_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<font color="Maroon" title="c9">z</font> = 
<span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c7">Y</font></span>)</span>,<font color="Maroon" title="c9">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon" title="c14">z'</font>
<b>by </b><i><a class="txt" href="prelamb.html#E3:33_1_2_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="prelamb.html#E5:33_1_2_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>
<b>hence </b><a NAME="E9:33_1_2_1"/>
<font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font>
 <b>by </b><i><a class="txt" href="prelamb.html#E3:33_1_2_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="prelamb.html#E5:33_1_2_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="txt" href="prelamb.html#E6:33_1_2_1"><i><font color="Green" title="E12">A6</font></i></a>, <a class="txt" href="prelamb.html#E7:33_1_2_1"><i><font color="Green" title="E13">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:33_1_2"/>
( not <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 &amp; <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c3">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">r2</font> )
 ;<br/>


</div>
