<?xml version="1.0"?>
<div class="add">

<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">V</font>, <font color="Olive" title="b2">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">f</font> being  <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">f</font>,<font color="Maroon" title="c1">a</font>) is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font>, <font color="Maroon" title="c3">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">f</font> being  <font color="Maroon" title="c2">V</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Olive" title="b1">f</font>,<font color="Maroon" title="c1">a</font>) is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be  <font color="Maroon" title="c2">V</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">a</font>) is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:88"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">  <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">a</font>) is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font></span><br/>

<a NAME="E2:88"/><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">(<span class="default"><a href="nomin_1.html#K14" title="NOMIN_1:func.14">namingSeq</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">f</font>,<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> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="nomin_1.html#D14" target="_self" onmouseover="rs('nomin_1/D14')" onmouseout="rh()">Def14</a></span>;<br/>
<a NAME="E3:88"/><span class="kw">then </span>
<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <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="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">a</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:88"/>
 <a href="nomin_1.html#K15" title="NOMIN_1:func.15">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c1">a</font>) is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88"><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>; <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>
