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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b3">h</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">g</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b3">h</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b3">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Olive" title="b2">g</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Olive" title="b2">g</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">h</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b1">h</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">h</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> )</span><br/>





<span class="lab"><font color="Green" title="E35">L1</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c4">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T42" target="_self" onmouseover="rs('rvsum_4/T42')" onmouseout="rh()">XFF</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" onmouseover="rs('afinsq_1/T27')" onmouseout="rh()">AFINSQ_1:27</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T42" target="_self" onmouseover="rs('rvsum_4/T42')" onmouseout="rh()">XFF</a></span>
;<br/>
<span class="lab"><font color="Green" title="E36">L2</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T39" target="_self" onmouseover="rs('rvsum_4/T39')" onmouseout="rh()">XFX</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" onmouseover="rs('afinsq_1/T27')" onmouseout="rh()">AFINSQ_1:27</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T43" target="_self" onmouseover="rs('rvsum_4/T43')" onmouseout="rh()">SFF</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T42" target="_self" onmouseover="rs('rvsum_4/T42')" onmouseout="rh()">XFF</a></span>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T41" target="_self" onmouseover="rs('rvsum_4/T41')" onmouseout="rh()">FFX</a></span>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T41" target="_self" onmouseover="rs('rvsum_4/T41')" onmouseout="rh()">FFX</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T41" target="_self" onmouseover="rs('rvsum_4/T41')" onmouseout="rh()">FFX</a></span>
<br/>.= 
<font color="Maroon" title="c4">h</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T32" onmouseover="rs('finseq_1/T32')" onmouseout="rh()">FINSEQ_1:32</a></span>
<br/>.= 
<font color="Maroon" title="c4">h</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T45" target="_self" onmouseover="rs('rvsum_4/T45')" onmouseout="rh()">SXX</a></span>
<br/>.= 
<font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T41" target="_self" onmouseover="rs('rvsum_4/T41')" onmouseout="rh()">FFX</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:98"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">h</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c3">g</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:98"><span class="lab"><font color="Green" title="E35">L1</font></span></a>, <a class="txt" href="#E2:98"><span class="lab"><font color="Green" title="E36">L2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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