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<span class="kw">let </span><font color="Maroon" title="c1">y</font>, <font color="Maroon" title="c2">X9</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Ch</font>, <font color="Olive" title="b2">F</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">Ch</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/> <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Olive" title="b2">F</font>,<font color="Olive" title="b1">Ch</font>,<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Olive" title="b2">F</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">Ch</font>, <font color="Maroon" title="c4">F</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:32"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font></span><br/>

<a NAME="E2:32"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
 <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font> or <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:32_1"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1"><span class="kw">now </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">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">Ch</font> &amp; <font color="Maroon" title="c3">Ch</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font> implies <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32_1_1"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c3">Ch</font>
 <span class="kw">and </span><br/><a NAME="E2:32_1_1"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<font color="Maroon" title="c3">Ch</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/><a NAME="E3:32_1_1"/>
<font color="Maroon" title="c3">Ch</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32_1_1"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:32_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<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="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E1:32_1_1"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></span>;<br/><a NAME="E5:32_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></span>;<br/><a NAME="E6:32_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E7:32_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:32_1_1"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></span>;<br/><span class="kw">hence </span><a NAME="E8:32_1_1"/>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E6:32_1_1"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="card_fin.html#D2" target="_self" title="CARD_FIN:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:32_1"/>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="card_fin.html#D2" target="_self" title="CARD_FIN:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:32"/>
 <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_fin.html#T29" target="_self" title="CARD_FIN:th.29">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:32"/>
 <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c3">Ch</font>,<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c4">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">Ch</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">X9</font></span>)</span>,<font color="Maroon" title="c1">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
