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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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"/><i><font color="Green" title="E30">A1</font></i>: 
( <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> &amp; <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> &amp; <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> )
 
<b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E2:69"/><b>then </b>
( <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> &amp; <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> )
 
<b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E4:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="prelamb.html#E41"><i><font color="Green" title="E19">Lm13</font></i></a></i>;<br/>
<a NAME="E5:69"/><b>then </b><i><font color="Green" title="E31">A2</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="prelamb.html#E42"><i><font color="Green" title="E20">Lm14</font></i></a></i>;<br/>
<a NAME="E6:69"/>
( <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="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> &amp; <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> )
 
<b>by </b><i><a class="txt" href="#E1:69"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E7:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E8:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E9:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="prelamb.html#E40"><i><font color="Green" title="E18">Lm12</font></i></a></i>;<br/>
<a NAME="E10:69"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="prelamb.html#E42"><i><font color="Green" title="E20">Lm14</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:69"/>
<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>
 <b>by </b><i><a class="txt" href="#E5:69"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="prelamb.html#D20" target="_self" title="PRELAMB:def.20">Def20</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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