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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <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"> for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">Bo1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo1</font>,<font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b4">Bo2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b5">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b4">Bo2</font>,<font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b2">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b4">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">Bo1</font>,<font color="Olive" title="b3">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b1">B</font>,<font color="Olive" title="b4">Bo2</font>,<font color="Olive" title="b5">yo2</font> holds <br/>( <font color="Olive" title="b2">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">Bo2</font> &amp; <font color="Olive" title="b3">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">yo2</font> )</span><br/><b>let </b><font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">Bo1</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"> for <font color="Olive" title="b1">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">Bo2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo2</font>,<font color="Maroon" title="c1">A</font>  st <font color="Maroon" title="c3">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Olive" title="b2">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Olive" title="b1">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Olive" title="b2">Bo2</font>,<font color="Olive" title="b3">yo2</font> holds <br/>( <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Bo2</font> &amp; <font color="Olive" title="b1">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">yo2</font> )</span><br/><b>let </b><font color="Maroon" title="c4">yo1</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Bo2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">Bo2</font>,<font color="Maroon" title="c1">A</font>  st <font color="Maroon" title="c3">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Olive" title="b1">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Olive" title="b1">Bo2</font>,<font color="Olive" title="b2">yo2</font> holds <br/>( <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">Bo2</font> &amp; <font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">yo2</font> )</span><br/><b>let </b><font color="Maroon" title="c5">Bo2</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"> for <font color="Olive" title="b1">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c5">Bo2</font>,<font color="Maroon" title="c1">A</font>  st <font color="Maroon" title="c3">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c5">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">Bo2</font>,<font color="Olive" title="b1">yo2</font> holds <br/>( <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Bo2</font> &amp; <font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">yo2</font> )</span><br/><b>let </b><font color="Maroon" title="c6">yo2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c5">Bo2</font>,<font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c5">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">Bo2</font>,<font color="Maroon" title="c6">yo2</font> implies ( <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Bo2</font> &amp; <font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">yo2</font> ) )</span><br/>











<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E9">AS</font></i>: 
( <font color="Maroon" title="c3">Bo1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp; <font color="Maroon" title="c5">Bo2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> &amp;  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">Bo2</font>,<font color="Maroon" title="c6">yo2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Bo2</font> &amp; <font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">yo2</font> )</span><br/>

<a NAME="E2:10"/><i><font color="Green" title="E10">P1</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo1</font> </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">Bo1</font>,<font color="Maroon" title="c4">yo1</font>
 
<b>by </b><i><a class="ref" href="petri_2.html#D1" target="_self" title="PETRI_2:def.1">DefX01</a>, <a class="txt" href="#E1:10"><i><font color="Green" title="E9">AS</font></i></a></i>;<br/>
<a NAME="E3:10"/><i><font color="Green" title="E11">P2</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">Bo2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">yo2</font> </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c5">Bo2</font>,<font color="Maroon" title="c6">yo2</font>
 
<b>by </b><i><a class="ref" href="petri_2.html#D1" target="_self" title="PETRI_2:def.1">DefX01</a>, <a class="txt" href="#E1:10"><i><font color="Green" title="E9">AS</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:10"/>
<font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Bo2</font>
 <b>by </b><i><a class="txt" href="petri_2.html#E9"><i><font color="Green" title="E7">Lm2</font></i></a>, <a class="txt" href="#E1:10"><i><font color="Green" title="E9">AS</font></i></a>, <a class="txt" href="#E2:10"><i><font color="Green" title="E10">P1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">yo2</font></span><br/>

<b>consider </b><font color="Maroon" title="c7">y0</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:10"/><i><font color="Green" title="E12">P4</font></i>: 
<font color="Maroon" title="c7">y0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo1</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="#E2:10"><i><font color="Green" title="E10">P1</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">y</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E8:10"/><i><font color="Green" title="E13">P5</font></i>: 
( <font color="Maroon" title="c7">y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> &amp; <font color="Maroon" title="c8">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo1</font> )
 <b>by </b><i><a class="txt" href="#E6:10"><i><font color="Green" title="E12">P4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">w</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E10:10"/><i><font color="Green" title="E14">P6</font></i>: 
( <font color="Maroon" title="c7">y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w</font> &amp; <font color="Maroon" title="c9">w</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">Bo2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">yo2</font> )
 <b>by </b><i><a class="txt" href="#E2:10"><i><font color="Green" title="E10">P1</font></i></a>, <a class="txt" href="#E3:10"><i><font color="Green" title="E11">P2</font></i></a>, <a class="txt" href="#E1:10"><i><font color="Green" title="E9">AS</font></i></a>, <a class="txt" href="#E6:10"><i><font color="Green" title="E12">P4</font></i></a></i>;<br/>
<b>thus </b><a NAME="E11:10"/>
<font color="Maroon" title="c4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">yo2</font>
 <b>by </b><i><a class="txt" href="petri_2.html#E9"><i><font color="Green" title="E7">Lm2</font></i></a>, <a class="txt" href="#E1:10"><i><font color="Green" title="E9">AS</font></i></a>, <a class="txt" href="#E2:10"><i><font color="Green" title="E10">P1</font></i></a>, <a class="txt" href="#E3:10"><i><font color="Green" title="E11">P2</font></i></a>, <a class="txt" href="#E8:10"><i><font color="Green" title="E13">P5</font></i></a>, <a class="txt" href="#E10:10"><i><font color="Green" title="E14">P6</font></i></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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