<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="prelamb.html#NM5" title="PRELAMB:NM.5">SynTypes_Calculus</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>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Olive" title="b3">z</font> <a href="prelamb.html#R3" title="PRELAMB:pred.3">&lt;==&gt;.</a> <font color="Olive" title="b1">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Olive" title="b3">z</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be   <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font> <a href="prelamb.html#R3" title="PRELAMB:pred.3">&lt;==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span></span><br/>







<a NAME="E1:69"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E2:69"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E3:69"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c4">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E4:69"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E5:69"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">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> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E6:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="prelamb.html#E41"><span class="lab"><font color="Green" title="E19">Lm11</font></span></a></span>;<br/>
<a NAME="E7:69"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A4</font></span>: 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="prelamb.html#E42"><span class="lab"><font color="Green" title="E20">Lm12</font></span></a></span>;<br/>
<a NAME="E8:69"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="txt" href="#E3:69"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E9:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<a NAME="E10:69"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">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> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></span>;<br/>
<a NAME="E11:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">z</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="prelamb.html#E40"><span class="lab"><font color="Green" title="E18">Lm10</font></span></a></span>;<br/>
<a NAME="E12:69"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="prelamb.html#E42"><span class="lab"><font color="Green" title="E20">Lm12</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:69"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font> <a href="prelamb.html#R3" title="PRELAMB:pred.3">&lt;==&gt;.</a> <font color="Maroon" title="c2">x</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Maroon" title="c4">z</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:69"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="ref" href="prelamb.html#D20" target="_self" title="PRELAMB:def.20">Def20</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/>


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