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<b>consider </b><font color="Maroon" title="c3">F</font> being    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/>
<a NAME="E2:5_1_1"/><i><font color="Green" title="E4">P2</font></i>: 
<font color="Maroon" title="c3">F</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="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> : <font color="Olive" title="b1">D</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> </span>}</span> 
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">z</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="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> : <font color="Olive" title="b1">D</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> </span>}</span>  implies <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> )</span><br/><b>assume </b><a NAME="E1:5_1_1_1"/>
<font color="Maroon" title="c4">z</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="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> : <font color="Olive" title="b1">D</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span></span><br/><a NAME="E2:5_1_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">D</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> st <br/>( <font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D</font> &amp; <font color="Olive" title="b1">D</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> )
 ;<br/><b>hence </b><a NAME="E3:5_1_1_1"/>
<font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:5_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="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> : <font color="Olive" title="b1">D</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> </span>}</span>  is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:5_1_1"><i><font color="Green" title="E4">P2</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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