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<b>let </b><font color="Maroon" title="c2">V1</font>, <font color="Maroon" title="c3">V2</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  &amp; <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  implies <font color="Maroon" title="c2">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:79_1_1"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )
 <b>and </b><br/><a NAME="E2:79_1_1"/><i><font color="Green" title="E42">A2</font></i>: 
( <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K2" title="ABCMIZ_1:func.2">Vars</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font> implies <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )</span><br/><b>assume </b><a NAME="E1:79_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/><a NAME="E2:79_1_1_1"/><b>then </b>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K6" title="ABCMIZ_1:func.6">a_Type</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K7" title="ABCMIZ_1:func.7">an_Adj</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_1.html#K8" title="ABCMIZ_1:func.8">a_Term</a>  )
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E1:79"><i><font color="Green" title="E40">A0</font></i></a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:79_1_1_1"/>
<font color="Maroon" title="c2">V1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="abcmiz_1.html#E1:79_1_1"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="abcmiz_1.html#E2:79_1_1"><i><font color="Green" title="E42">A2</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>hence </b><a NAME="E4:79_1_1"/>
<font color="Maroon" title="c2">V1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">V2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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