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<span class="kw">let </span><font color="Maroon" title="c1">v</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">D</font> being    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>  st <font color="Maroon" title="c1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">D</font> holds <br/> <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<font color="Maroon" title="c1">v</font>,<span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b3">D</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v</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">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">v</font></span>)</span></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">D</font> being    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>  st <font color="Maroon" title="c1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">D</font> holds <br/> <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">v</font>,<span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">D</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">v</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">D</font> be    <a href="nomin_1.html#M1" title="NOMIN_1:mode.1">NonatomicND</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">D</font> implies  <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">v</font>,<span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">D</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">v</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:92"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
<font color="Maroon" title="c1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">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="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">v</font>,<span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">D</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">v</font></span>)</span></span><br/>

<a NAME="E2:92"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c4">D</font> is   <a href="nomin_1.html#NM2" title="NOMIN_1:NM.2">TypeSSNominativeData</a> of <font color="Maroon" title="c2">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="nomin_1.html#K2" title="NOMIN_1:func.2">FNDSC</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nomin_1.html#T33" target="_self" onmouseover="rs('nomin_1/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<a NAME="E3:92"/><span class="kw">then </span>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c4">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D18" onmouseover="rs('relat_1/D18')" onmouseout="rh()">RELAT_1:def 18</a></span>;<br/>
<span class="kw">hence </span> <a href="nomin_1.html#K13" title="NOMIN_1:func.13">naming</a> (<font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">v</font>,<span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">D</font>)</span>)</span>) = 
<font color="Maroon" title="c1">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">D</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><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/>.= 
<font color="Maroon" title="c1">v</font> <a href="funcop_1.html#K17" title="FUNCOP_1:func.17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="nomin_1.html#D12" target="_self" onmouseover="rs('nomin_1/D12')" onmouseout="rh()">Def12</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/>


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