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<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp;  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span> &amp;  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span> &amp;  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> &amp;  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font> implies  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:34"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">and </span><br/><a NAME="E2:34"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">g</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <span class="kw">and </span><br/><a NAME="E3:34"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
 <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:34"/><span class="lab"><font color="Green" title="E35">A4</font></span>: 
 <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p2">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:34"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
 <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">and </span><br/><a NAME="E6:34"/><span class="lab"><font color="Green" title="E37">A6</font></span>: 
 <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">and </span><br/><a NAME="E7:34"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
 <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c2">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="calcul_1.html#R10" title="CALCUL_1:pred.10">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">A</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="calcul_1.html#D15" target="_self" title="CALCUL_1:def.15">CALCUL_1:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">J</font> being   <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b2">v</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> holds <br/><font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>  st <font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> holds <br/><font color="Maroon" title="c4">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">v</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> implies <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font> )</span><br/>





<span class="kw">assume </span><a NAME="E8:34"/><span class="lab"><font color="Green" title="E39">A8</font></span>: 
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/>

<a NAME="E9:34"/><span class="lab"><font color="Green" title="E40">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="calcul_1.html#T4" target="_self" title="CALCUL_1:th.4">Th4</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E41">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:34_1"/>
not <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/><a NAME="E2:34_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="valuat_1.html#T28" title="VALUAT_1:th.28">VALUAT_1:28</a></span>;<br/><a NAME="E3:34_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E9:34"><span class="lab"><font color="Green" title="E40">A9</font></span></a>, <a class="txt" href="#E8:34"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="calcul_1.html#T17" target="_self" title="CALCUL_1:th.17">Th17</a></span>;<br/><span class="kw">hence </span><a NAME="E4:34_1"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E7:34"><span class="lab"><font color="Green" title="E38">A7</font></span></a>, <a class="ref" href="calcul_1.html#D15" target="_self" title="CALCUL_1:def.15">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:34"/><span class="lab"><font color="Green" title="E42">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="calcul_1.html#T4" target="_self" title="CALCUL_1:th.4">Th4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:34_2"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <span class="p1">(<span class="default"><a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font></span><br/><a NAME="E2:34_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="calcul_1.html#R9" title="CALCUL_1:pred.9">|=</a>  <a href="calcul_1.html#K1" title="CALCUL_1:func.1">Ant</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:34"><span class="lab"><font color="Green" title="E42">A11</font></span></a>, <a class="txt" href="#E8:34"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="ref" href="calcul_1.html#T17" target="_self" title="CALCUL_1:th.17">Th17</a></span>;<br/><span class="kw">hence </span><a NAME="E3:34_2"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="ref" href="calcul_1.html#D15" target="_self" title="CALCUL_1:def.15">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:34"/>
<font color="Maroon" title="c4">J</font>,<font color="Maroon" title="c5">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="calcul_1.html#K2" title="CALCUL_1:func.2">Suc</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:34"><span class="lab"><font color="Green" title="E41">A10</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
