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<span class="kw">let </span><font color="Maroon" title="c1">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font>, <font color="Olive" title="b3">q1</font>, <font color="Olive" title="b4">q2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Olive" title="b3">q1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Olive" title="b1">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b4">q2</font> holds <br/>( <font color="Olive" title="b1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q1</font> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">q2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c3">p2</font>, <font color="Maroon" title="c4">q1</font>, <font color="Maroon" title="c5">q2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Maroon" title="c4">q1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Maroon" title="c2">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">q2</font> implies ( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c2">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">Q</font> = <font color="Maroon" title="c4">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">q2</font>;<br/>
<span class="kw">assume </span><a NAME="E1:192"/>
( <font color="Maroon" title="c2">p1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  &amp; <font color="Maroon" title="c4">q1</font> is <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">q2</font> or ( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> ) )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">x</font> = <font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c4">q1</font> as  <font color="Maroon" title="c1">m</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<a NAME="E3:192"/>
(  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">p1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p1</font> &amp;  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">q1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">q1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E4:192"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">B0</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:192"/><span class="lab"><font color="Green" title="E77">B1</font></span>: 
<font color="Maroon" title="c2">p1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">q2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font> &amp; <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font> )</span><br/>

<a NAME="E6:192"/>
( <font color="Maroon" title="c8">x</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> is  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  &amp; <font color="Maroon" title="c9">y</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> is  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a></span>)</span> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  )
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">p11</font> = <font color="Maroon" title="c2">p1</font>, <font color="Maroon" title="c11">q11</font> = <font color="Maroon" title="c4">q1</font> as   <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<span class="lab"><font color="Green" title="E78">Z0</font></span>: <font color="Maroon" title="c10">p11</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">q11</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c5">q2</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:192"><span class="lab"><font color="Green" title="E76">B0</font></span></a>, <a class="txt" href="#E5:192"><span class="lab"><font color="Green" title="E77">B1</font></span></a>, <a class="ref" href="finseq_6.html#T11" title="FINSEQ_6:th.11">FINSEQ_6:11</a></span>
<br/>.= 
<font color="Maroon" title="c11">q11</font> <a href="fomodel0.html#K13" title="FOMODEL0:func.13">null</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:192"><span class="lab"><font color="Green" title="E76">B0</font></span></a>, <a class="ref" href="finseq_6.html#T11" title="FINSEQ_6:th.11">FINSEQ_6:11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E9:192"/>
<font color="Maroon" title="c2">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font></span><br/>

<span class="kw">thus </span><a NAME="E10:192"/>
<font color="Maroon" title="c3">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:192"><span class="lab"><font color="Green" title="E78">Z0</font></span></a>, <a class="txt" href="#E5:192"><span class="lab"><font color="Green" title="E77">B1</font></span></a>, <a class="ref" href="finseq_1.html#T33" title="FINSEQ_1:th.33">FINSEQ_1:33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
