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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">V</font> being   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> <br/>  for <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">V</font>  st <font color="Maroon" title="c1">a</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b2">V</font>,<font color="Olive" title="b1">A</font> holds <br/> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Olive" title="b2">V</font>,<font color="Olive" title="b1">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   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> <br/>  for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">V</font>  st <font color="Maroon" title="c1">a</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b1">V</font>,<font color="Maroon" title="c2">A</font> holds <br/> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Olive" title="b1">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">V</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">v1</font>, <font color="Olive" title="b2">v2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">V</font>  st <font color="Maroon" title="c1">a</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font> holds <br/> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">v1</font>, <font color="Maroon" title="c5">v2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">V</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="c1">a</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font> implies  <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:90"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
<font color="Maroon" title="c1">a</font> is    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</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="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">f</font> = <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">g</font> =  <a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>);<br/>
<a NAME="E2:90"/><span class="lab"><font color="Green" title="E52">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" onmouseover="rs('finseq_1/T44')" onmouseout="rh()">FINSEQ_1:44</a></span>;<br/>
<a NAME="E3:90"/><span class="lab"><font color="Green" title="E53">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</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> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D14" target="_self" onmouseover="rs('nomin_1/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<a NAME="E4:90"/><span class="lab"><font color="Green" title="E54">A6</font></span>: 
<span class="p1">(<span class="default"><a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="ref" href="nomin_1.html#T58" target="_self" onmouseover="rs('nomin_1/T58')" onmouseout="rh()">Th58</a></span>;<br/>
<span class="lab"><font color="Green" title="E55">A7</font></span>: <span class="p1">(<span class="default"><a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
 <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span></span>)</span>,<font color="Maroon" title="c1">a</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#D14" target="_self" onmouseover="rs('nomin_1/D14')" onmouseout="rh()">Def14</a></span>
<br/>.= 
<font color="Maroon" title="c5">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="txt" href="#E1:90"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="nomin_1.html#D13" target="_self" onmouseover="rs('nomin_1/D13')" onmouseout="rh()">Def13</a></span>
;<br/>
<span class="kw">thus </span> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>) = 
 <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p1">(<span class="default"><span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c3">V</font>,<font color="Maroon" title="c2">A</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>,<font color="Maroon" title="c1">a</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="txt" href="#E3:90"><span class="lab"><font color="Green" title="E53">A5</font></span></a>, <a class="ref" href="nomin_1.html#D14" target="_self" onmouseover="rs('nomin_1/D14')" onmouseout="rh()">Def14</a></span>
<br/>.= 
<font color="Maroon" title="c4">v1</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v2</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <font color="Maroon" title="c1">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="txt" href="#E4:90"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="txt" href="#E5:90"><span class="lab"><font color="Green" title="E55">A7</font></span></a>, <a class="ref" href="nomin_1.html#D13" target="_self" onmouseover="rs('nomin_1/D13')" onmouseout="rh()">Def13</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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