<?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">T</font>, <font color="Olive" title="b2">X</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><br/> for <font color="Olive" title="b3">y</font>, <font color="Olive" title="b4">x</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 <font color="Olive" title="b1">T</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Olive" title="b3">y</font> &amp; <font color="Olive" title="b2">X</font> <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="Olive" title="b4">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="Olive" title="b5">z</font> holds <br/><span class="p1">(<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> <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="Olive" title="b3">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b4">x</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="Olive" title="b5">z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font>, <font color="Maroon" title="c3">X</font> be    <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>; <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>, <font color="Olive" title="b2">x</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>  st <font color="Maroon" title="c2">T</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Olive" title="b1">y</font> &amp; <font color="Maroon" title="c3">X</font> <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="Olive" title="b2">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="Olive" title="b3">z</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">T</font></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"><span class="p2">(<span class="default"><font color="Olive" title="b1">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b2">x</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="Olive" title="b3">z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">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"> ( <font color="Maroon" title="c2">T</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c3">X</font> <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="c5">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="c6">z</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">T</font></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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c5">x</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="c6">z</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:44"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c2">T</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c4">y</font>
 <span class="kw">and </span><br/><a NAME="E2:44"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<font color="Maroon" title="c3">X</font> <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="c5">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="c6">z</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="c3">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">T</font></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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c5">x</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="c6">z</font></span><br/>

<a NAME="E3:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <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="c5">x</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">H<sub>2</sub></font>(<font color="Maroon" title="c1">s</font>) <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c6">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></span>;<br/>
<a NAME="E4:44"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">T</font></span>)</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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c5">x</font></span>)</span></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">H<sub>2</sub></font>(<font color="Maroon" title="c1">s</font>) <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c6">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:44"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c2">T</font></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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c5">x</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="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</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>
