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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">p</font> being  <a href="rewrite2.html#V1" title="REWRITE2:attr.1">XFinSequence-yielding</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds <br/> ( <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="rewrite2.html#V1" title="REWRITE2:attr.1">XFinSequence-yielding</a>  <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="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>



<div><span class="lab"><font color="Green" title="E9">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">k</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> )</span><br/><span class="kw">assume </span><a NAME="E1:15_1"/>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</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"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> = 
<span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T32" title="AFINSQ_1:th.32">AFINSQ_1:32</a></span>
;<br/> <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><span class="kw">end;</span></div>
<a NAME="E2:15"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</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">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" title="REWRITE2:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:15"/>
<span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">^+</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</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">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/>

<div><span class="lab"><font color="Green" title="E10">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">k</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> )</span><br/><span class="kw">assume </span><a NAME="E1:15_2"/>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</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="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" title="REWRITE2:def.3">Def3</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">.</a> <font color="Maroon" title="c3">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T32" title="AFINSQ_1:th.32">AFINSQ_1:32</a></span>
;<br/> <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><span class="kw">end;</span></div>
<a NAME="E5:15"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></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">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" title="REWRITE2:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:15"/>
<font color="Maroon" title="c2">p</font> <a href="rewrite2.html#K3" title="REWRITE2:func.3">+^</a> <span class="p1">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</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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