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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="midsp_1.html#NM1" title="MIDSP_1:NM.1">MidSp</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">u</font>, <font color="Olive" title="b2">v</font> being   <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font>  ex <font color="Olive" title="b3">w</font> being   <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> ex <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Olive" title="b4">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b5">q</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">u</font>, <font color="Maroon" title="c3">v</font> be    <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">w</font> being   <a href="midsp_1.html#M1" title="MIDSP_1:mode.1">Vector</a> of <font color="Maroon" title="c1">M</font> ex <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Olive" title="b2">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">q</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>





<span class="kw">consider </span><font color="Maroon" title="c4">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span><span class="kw"> such that </span><br/><a NAME="E2:60"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#D8" target="_self" title="MIDSP_1:def.8">Def8</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span><span class="kw"> such that </span><br/><a NAME="E4:60"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#D8" target="_self" title="MIDSP_1:def.8">Def8</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E6:60"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> ,<font color="Maroon" title="c5">q</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="midsp_1.html#R1" title="MIDSP_1:pred.1">@@</a> <font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> ,<font color="Maroon" title="c6">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="midsp_1.html#T26" target="_self" title="MIDSP_1:th.26">Th26</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Olive" title="b1">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">q</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c7">p9</font> = <font color="Maroon" title="c4">p</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">q</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> st <br/>( <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">q</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">q</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c8">q9</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>; <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">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:60"/>
<font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E30">A1</font></span></a></span>; <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="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  &amp; <font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>

<a NAME="E8:60"/>
( <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  &amp; <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E9:60"/><span class="kw">then </span>
<font color="Maroon" title="c5">q</font> <a href="midsp_1.html#R2" title="MIDSP_1:pred.2">##</a> <font color="Maroon" title="c8">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="midsp_1.html#D6" target="_self" title="MIDSP_1:def.6">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:60"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="midsp_1.html#T42" target="_self" title="MIDSP_1:th.42">Th42</a></span>; <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="c7">p9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E11:60"/>
<font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> </span><br/>

<span class="kw">thus </span><a NAME="E12:60"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<font color="Maroon" title="c6">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">p9</font> <a href="midsp_1.html#K4" title="MIDSP_1:func.4">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">q9</font> <a href="midsp_1.html#K5" title="MIDSP_1:func.5">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="midsp_1.html#K7" title="MIDSP_1:func.7">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</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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