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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b2">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b2">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">e</font>,<font color="Olive" title="b1">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> holds <br/><font color="Olive" title="b2">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b1">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font>)</span>)</span>,<font color="Olive" title="b1">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c1">D</font><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b1">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c2">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">e</font> holds <br/><font color="Olive" title="b1">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b3">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</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">p</font>, <font color="Olive" title="b2">q</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c2">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">e</font> holds <br/><font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</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"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c2">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">e</font> implies <font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c2">e</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">e</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"> <font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">r</font> = <font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>);<br/>
<a NAME="E3:26"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="finseq_2.html#T72" onmouseover="rs('finseq_2/T72')" onmouseout="rh()">FINSEQ_2:72</a></span>;<br/>
<a NAME="E4:26"/><span class="lab"><font color="Green" title="E16">A4</font></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">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E5:26"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E6:26"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c5">q</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_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">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds  <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span><br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_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"> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:26_1_1_1"/>
( <font color="Maroon" title="c7">i</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="c4">p</font> or  not <font color="Maroon" title="c7">i</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="c4">p</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:26_1_1_1_1"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c7">i</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="c4">p</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"> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>) = 
<font color="Maroon" title="c3">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
<br/>.= 
<font color="Maroon" title="c3">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">q</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E1:26_1_1_1_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E1:26_1_1_1_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="funcop_1.html#T22" onmouseover="rs('funcop_1/T22')" onmouseout="rh()">FUNCOP_1:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E1:26_1_1_1_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
;<br/> <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:26_1_1_1_2"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
 not <font color="Maroon" title="c7">i</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="c4">p</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"> <font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>) = 
<font color="Maroon" title="c3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">e</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
<br/>.= 
<font color="Maroon" title="c2">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E1:26_1_1_1_2"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E1:26_1_1_1_2"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="setwop_2.html#T20" target="_self" onmouseover="rs('setwop_2/T20')" onmouseout="rh()">Th20</a></span>
;<br/> <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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E2:26_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T37" onmouseover="rs('funcop_1/T37')" onmouseout="rh()">FUNCOP_1:37</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>
<span class="kw">hence </span><a NAME="E8:26"/>
<font color="Maroon" title="c3">F</font> <a href="funcop_1.html#K6" title="FUNCOP_1:func.6">.:</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">e</font>)</span>)</span>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>)</span>)</span>,<font color="Maroon" title="c2">e</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" onmouseover="rs('funct_2/T63')" onmouseout="rh()">FUNCT_2:63</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>
