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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">P</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a><br/>  for <font color="Olive" title="b3">Q</font> being  <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Olive" title="b3">Q</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp; <font color="Olive" title="b1">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b3">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b1">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Olive" title="b1">R</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b3">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b1">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font>, <font color="Maroon" title="c3">P</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Q</font> being  <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Olive" title="b1">Q</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp; <font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b1">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Olive" title="b1">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">Q</font> be  <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">Q</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp; <font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  &amp;  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:128"/>
<font color="Maroon" title="c4">Q</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  or  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  or  not  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">QQ</font> = <font color="Maroon" title="c4">Q</font> as  <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">tQ</font> = <font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a> ;<br/>
<span class="kw">assume </span><a NAME="E3:128"/>
<font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a>  or  not  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">RR</font> = <font color="Maroon" title="c2">R</font> as  <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> ;<br/>
<span class="kw">assume </span><a NAME="E5:128"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> is  <a href="funct_1.html#V1" title="FUNCT_1:attr.1">Function-like</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">f</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<span class="lab"><font color="Green" title="E63">B0</font></span>: <font color="Maroon" title="c8">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>
<br/>.= 
<font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>
<br/>.= 
<font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c7">RR</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>
;<br/>
<a NAME="E8:128"/>
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">Y</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c7">RR</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c7">RR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fomodel0.html#T21" target="_self" title="FOMODEL0:th.21">Th21</a>, <a class="ref" href="relat_1.html#T30" title="RELAT_1:th.30">RELAT_1:30</a></span>;<br/>
<a NAME="E9:128"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">Z1</font></span>: 
<font color="Maroon" title="c7">RR</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c7">RR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T65" title="RELAT_1:th.65">RELAT_1:65</a></span>;<br/>
<span class="kw">assume </span><a NAME="E10:128"/>
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span><br/>

<a NAME="E11:128"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">B1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T27" title="RELAT_1:th.27">RELAT_1:27</a></span>;<br/>
<a NAME="E12:128"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></span>;<br/>
<a NAME="E13:128"/><span class="kw">then </span>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">P</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">QQ</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" title="RELAT_1:th.36">RELAT_1:36</a></span>;<br/>
<a NAME="E14:128"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:128"><span class="lab"><font color="Green" title="E65">B1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:128"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c4">Q</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Q</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a></span>)</span></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">*</a> <font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:128"><span class="lab"><font color="Green" title="E64">Z1</font></span></a>, <a class="txt" href="#E7:128"><span class="lab"><font color="Green" title="E63">B0</font></span></a>, <a class="txt" href="fomodel0.html#E87"><span class="lab"><font color="Green" title="E61">Lm47</font></span></a>, <a class="ref" href="relat_1.html#T29" title="RELAT_1:th.29">RELAT_1:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
