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<span class="kw">let </span><font color="Maroon" title="c1">s</font>, <font color="Maroon" title="c2">t</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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">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/> ( <font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Olive" title="b1">p</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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" 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"> ( <font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span> )</span><br/>





<div><span class="lab"><font color="Green" title="E9">A1</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">now </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">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> )</span><br/><span class="kw">assume </span><a NAME="E1:17_1"/>
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span><br/><a NAME="E2:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>;<br/><a NAME="E3:17_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> = 
<font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></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/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</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/></div><span class="kw">end;</span></div>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>
<br/>.= 
 <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"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D2" target="_self" onmouseover="rs('rewrite2/D2')" onmouseout="rh()">Def2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:17"/>
<font color="Maroon" title="c1">s</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K1" title="REWRITE2:func.1">^+</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="finseq_1.html#T13" onmouseover="rs('finseq_1/T13')" onmouseout="rh()">FINSEQ_1:13</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span><br/>

<div><span class="lab"><font color="Green" title="E10">A4</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_3"><span class="kw">now </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">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <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"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <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"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> )</span><br/><span class="kw">assume </span><a NAME="E1:17_3"/>
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <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"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span><br/><a NAME="E2:17_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A5</font></span>: 
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>;<br/><a NAME="E3:17_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A6</font></span>: 
<font color="Maroon" title="c4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_3"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_3"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></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/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17_3"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</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/></div><span class="kw">end;</span></div>
 <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"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite2.html#D3" target="_self" onmouseover="rs('rewrite2/D3')" onmouseout="rh()">Def3</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:17"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c2">t</font></span>)</span> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="rewrite2.html#K2" title="REWRITE2:func.2">+^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c1">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="finseq_1.html#T13" onmouseover="rs('finseq_1/T13')" onmouseout="rh()">FINSEQ_1:13</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/>


</div>
