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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">d</font>, <font color="Olive" title="b2">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="b3">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="b4">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b3">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b2">e</font>,<font color="Olive" title="b1">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e</font> holds <br/><font color="Olive" title="b3">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b2">e</font>)</span>)</span>,<font color="Olive" title="b1">d</font>) <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="b3">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b1">d</font>)</span>)</span>,<font color="Olive" title="b2">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">d</font>, <font color="Maroon" title="c3">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> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b1">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font> holds <br/><font color="Olive" title="b1">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</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="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>) <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#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font> holds <br/><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</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="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>) <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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">p</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"> ( <font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">e</font> implies <font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>) <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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>) )</span><br/>









<span class="kw">assume </span><a NAME="E1:27"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">d</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>) <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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_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="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>)</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">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="c6">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="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span><br/><a NAME="E1:27_1"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">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="c5">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="E2:27_1"/><span class="lab"><font color="Green" title="E16">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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</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="c5">p</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</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>, <a class="ref" href="finseq_2.html#T84" onmouseover="rs('finseq_2/T84')" onmouseout="rh()">FINSEQ_2:84</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="27_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="c4">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="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_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="E1:27_1_1_1"/>
( <font color="Maroon" title="c6">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="c5">p</font> or  not <font color="Maroon" title="c6">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="c5">p</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:27_1_1_1_1"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c6">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="c5">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="c4">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="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c4">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="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</font>) = 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</font>)
<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/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E1:27_1_1_1_1"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="funcop_1.html#T27" onmouseover="rs('funcop_1/T27')" onmouseout="rh()">FUNCOP_1:27</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E1:27_1_1_1_1"><span class="lab"><font color="Green" title="E17">A4</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="27_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:27_1_1_1_2"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 not <font color="Maroon" title="c6">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="c5">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="c4">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="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c4">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="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span>,<font color="Maroon" title="c2">d</font>) = 
<font color="Maroon" title="c4">F</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">d</font>)
<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/>.= 
<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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:27"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E2:27_1"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E1:27_1"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E1:27_1_1_1_2"><span class="lab"><font color="Green" title="E17">A5</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="E4:27_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p2">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">e</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T48" onmouseover="rs('funcop_1/T48')" onmouseout="rh()">FUNCOP_1:48</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="E3:27"/>
<font color="Maroon" title="c4">F</font> <a href="funcop_1.html#K9" title="FUNCOP_1:func.9">[:]</a> (<span class="p1">(<span class="default"><a href="setwop_2.html#K1" title="SETWOP_2:func.1">[#]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c3">e</font>)</span>)</span>,<font color="Maroon" title="c2">d</font>) <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="c4">F</font> <a href="finseqop.html#K2" title="FINSEQOP:func.2">[:]</a> (<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">d</font>)</span>)</span>,<font color="Maroon" title="c3">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/>


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