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<b>let </b><font color="Maroon" title="c1">N</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be    <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>;<br/><b>let </b><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c2">S</font>, <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c2">S</font>;<br/>





<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E39">A1</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F2</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <font color="Maroon" title="c2">S</font>;<br/><b>reconsider </b><font color="Maroon" title="c7">p'</font> = <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c8">q'</font> = <font color="Maroon" title="c6">q</font> as    <a href="ami_1.html#M1" title="AMI_1:mode.1">FinPartState</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="ami_3.html#T32" target="_self" title="AMI_3:th.32">Th32</a></i>;<br/><a NAME="E2:44_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F2</font> )
 <b>by </b><i><a class="txt" href="ami_3.html#E1:44"><i><font color="Green" title="E39">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:44_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">F2</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font>
 <b>by </b><i><a class="ref" href="ami_3.html#T19" target="_self" title="AMI_3:th.19">Th19</a></i>;<br/>


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