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<span class="kw">let </span><font color="Maroon" title="c1">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</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">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b4">la</font>, <font color="Olive" title="b5">lb</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Olive" title="b1">S</font>  st  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b4">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">A</font> &amp;  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b5">lb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">B</font> holds <br/>for <font color="Olive" title="b6">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">A</font><br/> for <font color="Olive" title="b7">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">B</font> holds  <font color="Olive" title="b4">la</font>,<font color="Olive" title="b5">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b6">a</font>,<font color="Olive" title="b7">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Olive" title="b1">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">N</font>; <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">A</font>, <font color="Olive" title="b2">B</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">la</font>, <font color="Olive" title="b4">lb</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">S</font>  st  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b3">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> &amp;  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b4">lb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> holds <br/>for <font color="Olive" title="b5">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font><br/> for <font color="Olive" title="b6">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">B</font> holds  <font color="Olive" title="b3">la</font>,<font color="Olive" title="b4">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</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"> for <font color="Olive" title="b1">la</font>, <font color="Olive" title="b2">lb</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">S</font>  st  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b1">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b2">lb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> holds <br/>for <font color="Olive" title="b3">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</font> holds  <font color="Olive" title="b1">la</font>,<font color="Olive" title="b2">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">la</font>, <font color="Maroon" title="c6">lb</font> be   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c6">lb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> implies for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</font> holds  <font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:112"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E2:112"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
 <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c6">lb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 ; <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">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font><br/> for <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</font> holds  <font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>; <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">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</font> holds  <font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Olive" title="b1">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</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">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font>;<br/>
<a NAME="E3:112"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A4</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">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="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:112_1"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</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="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="112_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="112_1_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="E1:112_1_1_1"/>
( ( <font color="Maroon" title="c5">la</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">la</font> ) or ( <font color="Maroon" title="c5">la</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">lb</font> ) or ( <font color="Maroon" title="c5">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">la</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:112"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E1:112_1"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="112_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:112_1_1_1_1"/><span class="lab"><font color="Green" title="E37">A6</font></span>: 
( <font color="Maroon" title="c5">la</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">la</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"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><div class="add"><a NAME="E2:112_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></span>;<br/><span class="kw">hence </span><a NAME="E3:112_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E1:112_1_1_1_1"><span class="lab"><font color="Green" title="E37">A6</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="112_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:112_1_1_1_2"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
( <font color="Maroon" title="c5">la</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">lb</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"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><div class="add"><a NAME="E2:112_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></span>;<br/><span class="kw">hence </span><a NAME="E3:112_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E1:112_1_1_1_2"><span class="lab"><font color="Green" title="E37">A7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="112_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:112_1_1_1_3"/><span class="lab"><font color="Green" title="E37">A8</font></span>: 
( <font color="Maroon" title="c5">la</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">lb</font> &amp; <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">la</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"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/><div class="add"><a NAME="E2:112_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">la</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_lang.html#T44" title="CQC_LANG:th.44">CQC_LANG:44</a></span>;<br/><a NAME="E3:112_1_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_1_1_1_3"><span class="lab"><font color="Green" title="E37">A8</font></span></a>, <a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>;<br/><span class="kw">hence </span><a NAME="E4:112_1_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="#E1:112_1_1_1_3"><span class="lab"><font color="Green" title="E37">A8</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:112_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <font color="Maroon" title="c2">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 ; <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">reconsider </span><font color="Maroon" title="c10">p</font> = <font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> as   <a href="ami_1.html#NM3" title="AMI_1:NM.3">PartState</a> of <font color="Maroon" title="c2">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:112"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E4:112"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="funct_1.html#D20" title="FUNCT_1:def.20">FUNCT_1:def 20</a>, <a class="ref" href="relat_1.html#D18" title="RELAT_1:def.18">RELAT_1:def 18</a></span>;<br/>
<a NAME="E6:112"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c10">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:112"/>
<font color="Maroon" title="c5">la</font>,<font color="Maroon" title="c6">lb</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">b</font> is   <a href="ami_1.html#NM4" title="AMI_1:NM.4">FinPartState</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</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>
