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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">T</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="b2">y</font>, <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">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="b2">y</font> &amp; <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b3">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="b4">z</font> holds <br/><font color="Olive" title="b1">T</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"><span class="p2">(<span class="default"><font color="Olive" title="b2">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b3">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="b4">z</font></span><br/><b>let </b><font color="Maroon" title="c2">T</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:()"><i><font color="Red">::  thesis: </font></i></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; <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/><font color="Maroon" title="c2">T</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"><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/><b>let </b><font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">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"> ( <font color="Maroon" title="c2">T</font> <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">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="c5">z</font> implies <font color="Maroon" title="c2">T</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c4">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="c5">z</font> )</span><br/>









<b>assume </b><a NAME="E1:46"/>
( <font color="Maroon" title="c2">T</font> <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">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="c5">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">T</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c4">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="c5">z</font></span><br/>

<a NAME="E2:46"/><b>then </b>
( <font color="Maroon" title="c2">T</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">s</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="c4">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="c5">z</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E3:46"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">s</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="c3">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c4">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="c5">z</font>
 
<b>by </b><i><a class="txt" href="prelamb.html#E37"><i><font color="Green" title="E15">Lm9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:46"/>
<font color="Maroon" title="c2">T</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c4">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="c5">z</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</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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