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<span class="kw">let </span><font color="Maroon" title="c5">F1</font>, <font color="Maroon" title="c6">F2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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></span>)</span>,<span class="p1">(<span class="default"><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></span>)</span>; <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">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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> holds <br/> ex <font color="Olive" title="b2">Bo2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font> ex <font color="Olive" title="b3">Bo1</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">Bo1</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="b2">Bo2</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo1</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b2">Bo2</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Bo2</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">yo2</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span> &amp; <font color="Olive" title="b4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">yo2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Bo1</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo2</font>,<font color="Olive" title="b5">yo2</font> &amp; <font color="Maroon" title="c5">F1</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="c1">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo1</font>,<font color="Olive" title="b4">yo1</font> ) ) &amp; ( 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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> holds <br/> ex <font color="Olive" title="b2">Bo2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font> ex <font color="Olive" title="b3">Bo1</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">Bo1</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="b2">Bo2</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo1</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b2">Bo2</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Bo2</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">yo2</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span> &amp; <font color="Olive" title="b4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">yo2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Bo1</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo2</font>,<font color="Olive" title="b5">yo2</font> &amp; <font color="Maroon" title="c6">F2</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="c1">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo1</font>,<font color="Olive" title="b4">yo1</font> ) ) implies <font color="Maroon" title="c5">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> holds <br/> ex <font color="Olive" title="b2">Bo21</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font> ex <font color="Olive" title="b3">Bo11</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">yo11</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b3">Bo11</font>,<font color="Maroon" title="c1">A1</font> ex <font color="Olive" title="b5">yo21</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo21</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo11</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b2">Bo21</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b3">Bo11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Bo21</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">yo21</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span> &amp; <font color="Olive" title="b4">yo11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">yo21</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Bo11</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo21</font>,<font color="Olive" title="b5">yo21</font> &amp; <font color="Maroon" title="c5">F1</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="c1">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo11</font>,<font color="Olive" title="b4">yo11</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> &amp; ( for <font color="Olive" title="b2">Bo2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font><br/> for <font color="Olive" title="b3">Bo1</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">B1</font><br/> for <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">Bo1</font>,<font color="Maroon" title="c1">A1</font><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="b2">Bo2</font>,<font color="Maroon" title="c2">A2</font>  holds <br/>(  not <font color="Olive" title="b3">Bo1</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  or  not <font color="Olive" title="b2">Bo2</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  or  not <font color="Olive" title="b3">Bo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Bo2</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">yo2</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span> or  not <font color="Olive" title="b4">yo1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">yo2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Bo1</font> or  not <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">Bo2</font>,<font color="Olive" title="b5">yo2</font> or  not <font color="Maroon" title="c6">F2</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="c1">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo1</font>,<font color="Olive" title="b4">yo1</font> ) ) ) or <font color="Maroon" title="c5">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:14_1_1"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> holds <br/> ex <font color="Olive" title="b2">Bo22</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font> ex <font color="Olive" title="b3">Bo12</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">yo12</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b3">Bo12</font>,<font color="Maroon" title="c1">A1</font> ex <font color="Olive" title="b5">yo22</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">Bo22</font>,<font color="Maroon" title="c2">A2</font> st <br/>( <font color="Olive" title="b3">Bo12</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b2">Bo22</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; <font color="Olive" title="b3">Bo12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Bo22</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">yo22</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span> &amp; <font color="Olive" title="b4">yo12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">yo22</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">Bo12</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="c2">A2</font>,<font color="Maroon" title="c4">B2</font>,<font color="Olive" title="b2">Bo22</font>,<font color="Olive" title="b5">yo22</font> &amp; <font color="Maroon" title="c6">F2</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="c1">A1</font>,<font color="Maroon" title="c3">B1</font>,<font color="Olive" title="b3">Bo12</font>,<font color="Olive" title="b4">yo12</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">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">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="c7">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="c2">A2</font>,<font color="Maroon" title="c4">B2</font> implies <font color="Maroon" title="c5">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:14_1_1_1"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c7">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="c2">A2</font>,<font color="Maroon" title="c4">B2</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">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">Bo21</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font>, <font color="Maroon" title="c9">Bo11</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="c10">yo11</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c9">Bo11</font>,<font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c11">yo21</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c8">Bo21</font>,<font color="Maroon" title="c2">A2</font><span class="kw"> such that </span><br/><a NAME="E3:14_1_1_1"/>
<font color="Maroon" title="c9">Bo11</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E4:14_1_1_1"/>
<font color="Maroon" title="c8">Bo21</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E5:14_1_1_1"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
<font color="Maroon" title="c9">Bo11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">Bo21</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">yo21</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
<font color="Maroon" title="c10">yo11</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">yo21</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c9">Bo11</font>
 <span class="kw">and </span><br/><a NAME="E7:14_1_1_1"/><span class="lab"><font color="Green" title="E16">A6</font></span>: 
<font color="Maroon" title="c7">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="Maroon" title="c8">Bo21</font>,<font color="Maroon" title="c11">yo21</font>
 <span class="kw">and </span><br/><a NAME="E8:14_1_1_1"/><span class="lab"><font color="Green" title="E17">A7</font></span>: 
<font color="Maroon" title="c5">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">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="Maroon" title="c9">Bo11</font>,<font color="Maroon" title="c10">yo11</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">Bo22</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c4">B2</font>, <font color="Maroon" title="c13">Bo12</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="c14">yo12</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c13">Bo12</font>,<font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c15">yo22</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c12">Bo22</font>,<font color="Maroon" title="c2">A2</font><span class="kw"> such that </span><br/><a NAME="E10:14_1_1_1"/>
<font color="Maroon" title="c13">Bo12</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E11:14_1_1_1"/>
<font color="Maroon" title="c12">Bo22</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1"/><span class="lab"><font color="Green" title="E18">A8</font></span>: 
<font color="Maroon" title="c13">Bo12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c12">Bo22</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">yo22</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <font color="Maroon" title="c1">A1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E13:14_1_1_1"/><span class="lab"><font color="Green" title="E19">A9</font></span>: 
<font color="Maroon" title="c14">yo12</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">yo22</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c13">Bo12</font>
 <span class="kw">and </span><br/><a NAME="E14:14_1_1_1"/><span class="lab"><font color="Green" title="E20">A10</font></span>: 
<font color="Maroon" title="c7">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="Maroon" title="c12">Bo22</font>,<font color="Maroon" title="c15">yo22</font>
 <span class="kw">and </span><br/><a NAME="E15:14_1_1_1"/><span class="lab"><font color="Green" title="E21">A11</font></span>: 
<font color="Maroon" title="c6">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">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="Maroon" title="c13">Bo12</font>,<font color="Maroon" title="c14">yo12</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E1:14_1_1_1"><span class="lab"><font color="Green" title="E13">A3</font></span></a></span>;<br/><a NAME="E16:14_1_1_1"/><span class="lab"><font color="Green" title="E22">A12</font></span>: 
<font color="Maroon" title="c11">yo21</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c15">yo22</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="ref" href="petri_2.html#T3" target="_self" title="PETRI_2:th.3">Th3</a></span>;<br/><a NAME="E17:14_1_1_1"/>
<font color="Maroon" title="c8">Bo21</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Bo22</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E16">A6</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="ref" href="petri_2.html#T3" target="_self" title="PETRI_2:th.3">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E18:14_1_1_1"/>
<font color="Maroon" title="c5">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E19">A9</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E22">A12</font></span></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="E4:14_1_1"/>
<font color="Maroon" title="c5">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</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/>


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