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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span> ex <font color="Olive" title="b1">D</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> st <br/>( <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">D</font>) );<br/>
<a NAME="E1:101_1_1"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">d</font> where <font color="Olive" title="b2">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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="b2">d</font> </span> } </span>  holds <br/> ex <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</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"> ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span>  implies  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Olive" title="b1">y</font>] ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:101_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </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">  ex <font color="Olive" title="b1">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">d</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font><span class="kw"> such that </span><br/><a NAME="E3:101_1_1_1"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E4:101_1_1_1"/>
<font color="Maroon" title="c3">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="c6">d</font>
 ;<br/>
<span class="kw">take </span>
 <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c6">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#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c6">d</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>, <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c6">d</font>)] )</span><br/>

<span class="kw">thus </span><a NAME="E5:101_1_1_1"/>
(  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c6">d</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>, <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c6">d</font>)] )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1_1_1"><span class="lab"><font color="Green" title="E56">A2</font></span></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">consider </span><font color="Maroon" title="c5">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E3:101_1_1"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span> 
 <span class="kw">and </span><br/><a NAME="E4:101_1_1"/><span class="lab"><font color="Green" title="E57">A4</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c5">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)
 <span class="kw">and </span><br/><a NAME="E5:101_1_1"/><span class="lab"><font color="Green" title="E58">A5</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">d</font> where <font color="Olive" title="b2">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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="b2">d</font> </span> } </span>  holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_1.html#S6" onmouseover="rs('funct_1/S6')" onmouseout="rh()">FUNCT_1:sch 6</a>(<a class="txt" href="#E1:101_1_1"><span class="lab"><font color="Green" title="E55">A1</font></span></a>);<br/></span>
<a NAME="E6:101_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="101_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</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"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:101_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span><br/>

<a NAME="E2:101_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">d</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> st <br/>( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c3">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> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:101_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c5">f</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1_1"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="txt" href="#E4:101_1_1"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="ref" href="relset_1.html#T4" onmouseover="rs('relset_1/T4')" onmouseout="rh()">RELSET_1:4</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">f</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="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span>  &amp; (  for <font color="Olive" title="b1">D</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b1">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</font> holds <br/><font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">D</font>) ) )</span><br/>

<span class="kw">thus </span><a NAME="E8:101_1_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">d</font> where <font color="Olive" title="b1">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font> : <font color="Maroon" title="c3">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> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1_1"><span class="lab"><font color="Green" title="E56">A3</font></span></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">  for <font color="Olive" title="b1">D</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">A</font>  st <font color="Olive" title="b1">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</font> holds <br/><font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">D</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">D</font> be    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c7">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</font> implies <font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c7">D</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E9:101_1_1"/>
<font color="Maroon" title="c7">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">f</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="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c7">D</font>)</span><br/>

<a NAME="E10:101_1_1"/><span class="kw">then </span>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">D</font>,<font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">D</font>]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:101_1_1"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="txt" href="#E5:101_1_1"><span class="lab"><font color="Green" title="E58">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:101_1_1"/>
<font color="Maroon" title="c6">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c7">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"> verum</span><br/>


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