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<b>let </b><font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c2">A2</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">B1</font>, <font color="Olive" title="b2">B2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A2</font> &amp; <font color="Olive" title="b1">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B2</font> holds <br/> ex <font color="Olive" title="b3">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Olive" title="b1">B1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Olive" title="b2">B2</font> st <br/>for <font color="Olive" title="b4">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Olive" title="b1">B1</font> holds <br/> ex <font color="Olive" title="b5">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">B1</font> ex <font color="Olive" title="b6">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b5">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <font color="Olive" title="b7">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b5">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b5">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b6">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b7">yo2</font> &amp; <font color="Olive" title="b4">x</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">A1</font>,<font color="Olive" title="b1">B1</font>,<font color="Olive" title="b5">Bo</font>,<font color="Olive" title="b6">yo1</font> &amp; <font color="Olive" title="b3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">x</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="c2">A2</font>,<font color="Olive" title="b2">B2</font>,<font color="Olive" title="b5">Bo</font>,<font color="Olive" title="b7">yo2</font> )</span><br/><b>let </b><font color="Maroon" title="c3">B1</font>, <font color="Maroon" title="c4">B2</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="c1">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A2</font> &amp; <font color="Maroon" title="c3">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B2</font> implies  ex <font color="Olive" title="b1">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> st <br/>for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> holds <br/> ex <font color="Olive" title="b3">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font> ex <font color="Olive" title="b4">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b3">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <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="b3">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">yo2</font> &amp; <font color="Olive" title="b2">x</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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo</font>,<font color="Olive" title="b4">yo1</font> &amp; <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b3">Bo</font>,<font color="Olive" title="b5">yo2</font> ) )</span><br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E10">AS</font></i>: 
( <font color="Maroon" title="c1">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A2</font> &amp; <font color="Maroon" title="c3">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">F</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> st <br/>for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> holds <br/> ex <font color="Olive" title="b3">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font> ex <font color="Olive" title="b4">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b3">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <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="b3">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b4">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">yo2</font> &amp; <font color="Olive" title="b2">x</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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo</font>,<font color="Olive" title="b4">yo1</font> &amp; <font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b3">Bo</font>,<font color="Olive" title="b5">yo2</font> )</span><br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font> ex <font color="Olive" title="b2">yo1</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <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="b1">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b1">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b2">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">yo2</font> &amp; $1 <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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b1">Bo</font>,<font color="Olive" title="b2">yo1</font> &amp; $2 <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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b1">Bo</font>,<font color="Olive" title="b3">yo2</font> );<br/>
<div><i><font color="Green" title="E11">P1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">x</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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> implies  ex <font color="Olive" title="b1">D2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">D2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Olive" title="b1">D2</font>] ) )</span><br/><b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">D2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">D2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Olive" title="b1">D2</font>] )</span><br/><a NAME="E2:11_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="c3">B1</font>,<font color="Maroon" title="c1">A1</font></span>)</span> st <br/>( <font color="Maroon" title="c5">x</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">A1</font>,<font color="Maroon" title="c3">B1</font> )
 ;<br/><b>then reconsider </b><font color="Maroon" title="c6">D1</font> = <font color="Maroon" title="c5">x</font> as    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> ;<br/><b>consider </b><font color="Maroon" title="c7">Bo</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font>, <font color="Maroon" title="c8">yo1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c1">A1</font><b> such that </b><br/><a NAME="E5:11_1"/><i><font color="Green" title="E12">P2</font></i>: 
( <font color="Maroon" title="c7">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c6">D1</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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c8">yo1</font> )
 <b>by </b><i><a class="ref" href="petri_2.html#D2" target="_self" title="PETRI_2:def.2">Def21</a></i>;<br/><a NAME="E6:11_1"/><i><font color="Green" title="E13">D13</font></i>: 
<font color="Maroon" title="c7">Bo</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B2</font>
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E10">AS</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">yo2</font> = <font color="Maroon" title="c8">yo1</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c2">A2</font> <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E10">AS</font></i></a>, <a class="ref" href="funct_2.html#T9" title="FUNCT_2:th.9">FUNCT_2:9</a></i>;<br/><b>set </b><font color="Maroon" title="c10">D2</font> =  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c9">yo2</font>;<br/><a NAME="E8:11_1"/><i><font color="Green" title="E14">XXX</font></i>: 
 <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c9">yo2</font> is    <a href="petri_2.html#M1" title="PETRI_2:mode.1">thin_cylinder</a> of <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font>
 <b>by </b><i><a class="txt" href="#E5:11_1"><i><font color="Green" title="E12">P2</font></i></a>, <a class="txt" href="#E6:11_1"><i><font color="Green" title="E13">D13</font></i></a>, <a class="ref" href="petri_2.html#D2" target="_self" title="PETRI_2:def.2">Def21</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">D2</font> =  <a href="petri_2.html#K1" title="PETRI_2:func.1">cylinder0</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Maroon" title="c7">Bo</font>,<font color="Maroon" title="c9">yo2</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><b>take </b><font color="Maroon" title="c12">D2</font> = <font color="Maroon" title="c11">D2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c12">D2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c12">D2</font>] )</span><br/><b>thus </b><a NAME="E10:11_1"/>
( <font color="Maroon" title="c12">D2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c12">D2</font>] )
 <b>by </b><i><a class="txt" href="#E5:11_1"><i><font color="Green" title="E12">P2</font></i></a>, <a class="txt" href="#E8:11_1"><i><font color="Green" title="E14">XXX</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/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c5">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font>, <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c4">B2</font><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green" title="E12">P2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> 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>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1" title="FUNCT_2:sch.1">FUNCT_2:sch 1</a>(<a class="txt" href="#E2:11"><i><font color="Green" title="E11">P1</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c5">F</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">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> holds <br/> ex <font color="Olive" title="b2">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font> ex <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">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <font color="Olive" title="b4">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b2">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b3">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">yo2</font> &amp; <font color="Olive" title="b1">x</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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b2">Bo</font>,<font color="Olive" title="b3">yo1</font> &amp; <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> <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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo</font>,<font color="Olive" title="b4">yo2</font> )</span><br/>

<b>thus </b><a NAME="E5:11"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="petri_2.html#K2" title="PETRI_2:func.2">thin_cylinders</a> <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c3">B1</font> holds <br/> ex <font color="Olive" title="b2">Bo</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font> ex <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">Bo</font>,<font color="Maroon" title="c1">A1</font> ex <font color="Olive" title="b4">yo2</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b2">Bo</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Olive" title="b3">yo1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">yo2</font> &amp; <font color="Olive" title="b1">x</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">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b2">Bo</font>,<font color="Olive" title="b3">yo1</font> &amp; <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> <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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo</font>,<font color="Olive" title="b4">yo2</font> )
 <b>by </b><i><a class="txt" href="#E4:11"><i><font color="Green" title="E12">P2</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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