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<span class="kw">let </span><font color="Maroon" title="c1">Y</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="partit1.html#K1" title="PARTIT1:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</font></span>)</span><br/> for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">a</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> <br/> for <font color="Olive" title="b4">PA</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b2">u</font> <a href="bvfunc_2.html#R3" title="BVFUNC_2:pred.3">is_independent_of</a> <font color="Olive" title="b4">PA</font>,<font color="Olive" title="b1">G</font> holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Olive" title="b3">a</font></span>)</span>,<font color="Olive" title="b4">PA</font>,<font color="Olive" title="b1">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">PA</font>,<font color="Olive" title="b1">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="partit1.html#K1" title="PARTIT1:func.1">PARTITIONS</a> <font color="Maroon" title="c1">Y</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">u</font>, <font color="Olive" title="b2">a</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> <br/> for <font color="Olive" title="b3">PA</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">u</font> <a href="bvfunc_2.html#R3" title="BVFUNC_2:pred.3">is_independent_of</a> <font color="Olive" title="b3">PA</font>,<font color="Maroon" title="c2">G</font> holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b3">PA</font>,<font color="Maroon" title="c2">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">a</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</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">PA</font> being   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Maroon" title="c3">u</font> <a href="bvfunc_2.html#R3" title="BVFUNC_2:pred.3">is_independent_of</a> <font color="Olive" title="b1">PA</font>,<font color="Maroon" title="c2">G</font> holds <br/> <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Olive" title="b1">PA</font>,<font color="Maroon" title="c2">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c4">a</font>,<font color="Olive" title="b1">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">PA</font> be    <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of <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="c3">u</font> <a href="bvfunc_2.html#R3" title="BVFUNC_2:pred.3">is_independent_of</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font> implies  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> )</span><br/>









<span class="kw">consider </span><font color="Maroon" title="c6">k3</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E2:37"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">k3</font>
 <span class="kw">and </span><br/><a NAME="E3:37"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">k3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">and </span><br/><a NAME="E4:37"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">k3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">k4</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E6:37"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">k4</font>
 <span class="kw">and </span><br/><a NAME="E7:37"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c7">k4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Y</font>
 <span class="kw">and </span><br/><a NAME="E8:37"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">k4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D2" title="FUNCT_2:def.2">FUNCT_2:def 2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E9:37"/>
<font color="Maroon" title="c3">u</font> <a href="bvfunc_2.html#R3" title="BVFUNC_2:pred.3">is_independent_of</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span><br/>

<a NAME="E10:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A5</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#R2" title="BVFUNC_1:pred.2">is_dependent_of</a>  <a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_2.html#D8" target="_self" title="BVFUNC_2:def.8">Def8</a></span>;<br/>
<a NAME="E11:37"/>
for <font color="Olive" title="b1">z</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> holds  <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span><br/>

<a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E13">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D7" title="BVFUNC_1:def.7">BVFUNC_1:def 7</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_1_1"/>
( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  or (  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) or (  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_1"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span><br/><div class="add"><a NAME="E2:37_1_1_1"/><span class="lab"><font color="Green" title="E15">A8</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1_1_1_1"/><span class="lab"><font color="Green" title="E16">A9</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D7" title="BVFUNC_1:def.7">BVFUNC_1:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_1"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E1:37_1_1_1_1"><span class="lab"><font color="Green" title="E16">A9</font></span></a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" title="BINARITH:th.19">BINARITH:19</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:37_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <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="E3:37_1_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_1"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="ref" href="bvfunc_1.html#D19" title="BVFUNC_1:def.19">BVFUNC_1:def 19</a></span>;<br/><a NAME="E4:37_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="ref" href="binarith.html#T19" title="BINARITH:th.19">BINARITH:19</a></span>;<br/><span class="kw">hence </span><a NAME="E5:37_1_1_1"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1_1"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="ref" href="bvfunc_1.html#D19" title="BVFUNC_1:def.19">BVFUNC_1:def 19</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_2"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
(  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span><br/><div class="add"><a NAME="E2:37_1_1_2"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1_1_2_1"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span> <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bvfunc_1.html#D7" title="BVFUNC_1:def.7">BVFUNC_1:def 7</a></span>
<br/>.= 
<a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E1:37_1_1_2_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a></span>
<br/>.= 
 <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" title="BINARITH:th.19">BINARITH:19</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:37_1_1_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ; <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="E3:37_1_1_2"/>
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/><a NAME="E4:37_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E1:37_1_1_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a></span>;<br/><a NAME="E5:37_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="binarith.html#T19" title="BINARITH:th.19">BINARITH:19</a></span>;<br/><span class="kw">hence </span><a NAME="E6:37_1_1_2"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1_1_2"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="bvfunc_1.html#D19" title="BVFUNC_1:def.19">BVFUNC_1:def 19</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:37_1_1_3"/><span class="lab"><font color="Green" title="E14">A13</font></span>: 
(  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) &amp;  ex <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp; not <font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font><span class="kw"> such that </span><br/><a NAME="E3:37_1_1_3"/><span class="lab"><font color="Green" title="E15">A14</font></span>: 
<font color="Maroon" title="c9">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:37_1_1_3"/><span class="lab"><font color="Green" title="E16">A15</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c10">x1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">Y</font><span class="kw"> such that </span><br/><a NAME="E6:37_1_1_3"/><span class="lab"><font color="Green" title="E17">A16</font></span>: 
<font color="Maroon" title="c10">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:37_1_1_3"/><span class="lab"><font color="Green" title="E18">A17</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_3"><span class="lab"><font color="Green" title="E14">A13</font></span></a></span>;<br/><a NAME="E8:37_1_1_3"/>
<font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">x2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E6:37_1_1_3"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="txt" href="#E3:37_1_1_3"><span class="lab"><font color="Green" title="E15">A14</font></span></a>, <a class="ref" href="bvfunc_1.html#D18" title="BVFUNC_1:def.18">BVFUNC_1:def 18</a></span>;<br/><a NAME="E9:37_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A18</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_1_1_3"><span class="lab"><font color="Green" title="E16">A15</font></span></a>, <a class="ref" href="xboolean.html#D3" title="XBOOLEAN:def.3">XBOOLEAN:def 3</a></span>;<br/><a NAME="E10:37_1_1_3"/><span class="lab"><font color="Green" title="E20">A19</font></span>: 
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1_1_3"><span class="lab"><font color="Green" title="E14">A13</font></span></a>, <a class="ref" href="bvfunc_1.html#D19" title="BVFUNC_1:def.19">BVFUNC_1:def 19</a></span>;<br/><a NAME="E11:37_1_1_3"/>
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bvfunc_1.html#K19" title="BVFUNC_1:func.19">EqClass</a> <font color="Maroon" title="c8">z</font>,<span class="p1">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#D8" title="EQREL_1:def.8">EQREL_1:def 8</a></span>;<br/><a NAME="E12:37_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A20</font></span>: 
<font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">u</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E6:37_1_1_3"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="ref" href="bvfunc_1.html#D18" title="BVFUNC_1:def.18">BVFUNC_1:def 18</a></span>;<br/><a NAME="E13:37_1_1_3"/>
<font color="Maroon" title="c4">a</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:37_1_1_3"><span class="lab"><font color="Green" title="E18">A17</font></span></a>, <a class="ref" href="xboolean.html#D3" title="XBOOLEAN:def.3">XBOOLEAN:def 3</a></span>;<br/><a NAME="E14:37_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  <a href="xboolean.html#K5" title="XBOOLEAN:func.5">'or'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:37_1_1_3"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="ref" href="bvfunc_1.html#D7" title="BVFUNC_1:def.7">BVFUNC_1:def 7</a></span>;<br/><span class="kw">hence </span><a NAME="E15:37_1_1_3"/>
<span class="p1">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p2">(<span class="default"><a href="bvfunc_1.html#K20" title="BVFUNC_1:func.20">B_INF</a> <font color="Maroon" title="c4">a</font>,<span class="p3">(<span class="default"><a href="bvfunc_2.html#K5" title="BVFUNC_2:func.5">CompF</a> <font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E10:37_1_1_3"><span class="lab"><font color="Green" title="E20">A19</font></span></a>, <a class="txt" href="#E6:37_1_1_3"><span class="lab"><font color="Green" title="E17">A16</font></span></a>, <a class="txt" href="#E9:37_1_1_3"><span class="lab"><font color="Green" title="E19">A18</font></span></a>, <a class="txt" href="#E12:37_1_1_3"><span class="lab"><font color="Green" title="E21">A20</font></span></a>, <a class="ref" href="bvfunc_1.html#D19" title="BVFUNC_1:def.19">BVFUNC_1:def 19</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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E12:37"/><span class="kw">then </span>
for <font color="Olive" title="b1">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Y</font> holds <br/><font color="Maroon" title="c6">k3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">k4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E10">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:37"/>
 <a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <font color="Maroon" title="c4">a</font></span>)</span>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">u</font> <a href="bvfunc_1.html#K7" title="BVFUNC_1:func.7">'or'</a> <span class="p1">(<span class="default"><a href="bvfunc_2.html#K6" title="BVFUNC_2:func.6">All</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">PA</font>,<font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</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>
