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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> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font>  st  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Olive" title="b1">x</font> holds <br/>(  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Olive" title="b2">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Olive" title="b1">x</font></span>)</span> &amp;  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b2">y</font> )</span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</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"> (  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c2">x</font> implies (  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp;  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <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#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font> ) )</span><br/>





<a NAME="E1:61"/>
<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>
 
<b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</a></i>;<br/>
<a NAME="E2:61"/><b>then </b><i><font color="Green" title="E29">A1</font></i>: 
( <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="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="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> <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="c3">y</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/>
<b>assume </b><a NAME="E3:61"/>
<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="c2">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp;  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <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#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font> )</span><br/>

<a NAME="E4:61"/><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> <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="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Maroon" title="c2">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="c3">y</font> &amp; <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> <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="c2">x</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</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></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="c3">y</font> )
 
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="prelamb.html#E34"><i><font color="Green" title="E12">Lm6</font></i></a>, <a class="txt" href="prelamb.html#E38"><i><font color="Green" title="E16">Lm10</font></i></a></i>;<br/>
<a NAME="E5:61"/><b>then </b>
( <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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Maroon" title="c2">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="c3">y</font> &amp; <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#K1" title="PRELAMB:func.1">\</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> <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="c3">y</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/>
<b>hence </b><a NAME="E6:61"/>
(  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <a href="prelamb.html#R2" title="PRELAMB:pred.2">==&gt;.</a> <font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Maroon" title="c2">x</font></span>)</span> &amp;  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> <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#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Maroon" title="c3">y</font> )
 <b>by </b><i><a class="ref" href="prelamb.html#D19" target="_self" title="PRELAMB:def.19">Def19</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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