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<b>let </b><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">C</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"> for <font color="Olive" title="b1">K</font>, <font color="Olive" title="b2">L</font>, <font color="Olive" title="b3">M</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span> holds  <font color="Olive" title="b1">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Olive" title="b3">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Olive" title="b3">M</font></span><br/><b>let </b><font color="Maroon" title="c3">K</font>, <font color="Maroon" title="c4">L</font>, <font color="Maroon" title="c5">M</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span><br/>





<a NAME="E1:31"/><i><font color="Green" title="E23">A1</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> &amp; <font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c3">K</font> &amp; <font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">M</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font> &amp; <font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c3">K</font> )
 
<b>by </b><i><a class="ref" href="substlat.html#T3" target="_self" title="SUBSTLAT:th.3">Th3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">K</font>, <font color="Maroon" title="c7">L</font>, <font color="Maroon" title="c8">M</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span><br/><a NAME="E1:31_1"/><i><font color="Green" title="E24">A2</font></i>: 
( <font color="Maroon" title="c6">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c7">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c8">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="ref" href="finsub_1.html#D5" title="FINSUB_1:def.5">FINSUB_1:def 5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">a</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="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span>)</span> implies <font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font> )</span><br/><b>assume </b><a NAME="E1:31_1_1"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span><br/><b>then consider </b><font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c11">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:31_1_1"/><i><font color="Green" title="E26">A4</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">K</font>
 <b>and </b><br/><a NAME="E4:31_1_1"/><i><font color="Green" title="E27">A5</font></i>: 
<font color="Maroon" title="c11">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font>
 <b>and </b><br/><a NAME="E5:31_1_1"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="ref" href="substlat.html#T15" target="_self" title="SUBSTLAT:th.15">Th15</a></i>;<br/><a NAME="E6:31_1_1"/>
<font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="ref" href="finsub_1.html#D5" title="FINSUB_1:def.5">FINSUB_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E8:31_1_1"/><i><font color="Green" title="E29">A7</font></i>: 
( <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c12">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">V</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c12">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">C</font> )
 <b>by </b><i><a class="txt" href="substlat.html#E1:31_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="partfun1.html#D5" title="PARTFUN1:def.5">PARTFUN1:def 5</a></i>;<br/><b>consider </b><font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c14">c1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E10:31_1_1"/><i><font color="Green" title="E30">A8</font></i>: 
<font color="Maroon" title="c13">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">L</font>
 <b>and </b><br/><a NAME="E11:31_1_1"/><i><font color="Green" title="E31">A9</font></i>: 
<font color="Maroon" title="c14">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">M</font>
 <b>and </b><br/><a NAME="E12:31_1_1"/><i><font color="Green" title="E32">A10</font></i>: 
<font color="Maroon" title="c11">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c14">c1</font>
 <b>by </b><i><a class="txt" href="substlat.html#E4:31_1_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="substlat.html#T15" target="_self" title="SUBSTLAT:th.15">Th15</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">b'</font> = <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c16">b1'</font> = <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c17">c1'</font> = <font color="Maroon" title="c14">c1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="txt" href="substlat.html#E1:31_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="substlat.html#E3:31_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="substlat.html#E10:31_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="substlat.html#E11:31_1_1"><i><font color="Green" title="E31">A9</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">b2</font> = <font color="Maroon" title="c10">b</font>, <font color="Maroon" title="c19">b12</font> = <font color="Maroon" title="c13">b1</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="txt" href="substlat.html#E1:31_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="substlat.html#E3:31_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="substlat.html#E10:31_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="partfun1.html#T120" title="PARTFUN1:th.120">PARTFUN1:120</a></i>;<br/><a NAME="E15:31_1_1"/><i><font color="Green" title="E33">A11</font></i>: 
( <font color="Maroon" title="c10">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font> &amp; <font color="Maroon" title="c11">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E16:31_1_1"/>
<font color="Maroon" title="c13">b1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="txt" href="substlat.html#E12:31_1_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E17:31_1_1"/><b>then </b><i><font color="Green" title="E34">A12</font></i>: 
<font color="Maroon" title="c13">b1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="txt" href="substlat.html#E15:31_1_1"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E18:31_1_1"/><b>then </b><i><font color="Green" title="E35">A13</font></i>: 
<font color="Maroon" title="c15">b'</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="txt" href="substlat.html#E5:31_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="substlat.html#E8:31_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="substlat.html#E15:31_1_1"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></i>;<br/><a NAME="E19:31_1_1"/><i><font color="Green" title="E36">A14</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c14">c1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c13">b1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c14">c1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>;<br/><a NAME="E20:31_1_1"/>
<font color="Maroon" title="c15">b'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c16">b1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b'</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="txt" href="substlat.html#E18:31_1_1"><i><font color="Green" title="E35">A13</font></i></a>, <a class="ref" href="funct_4.html#T31" title="FUNCT_4:th.31">FUNCT_4:31</a></i>;<br/><a NAME="E21:31_1_1"/><b>then </b>
<font color="Maroon" title="c18">b2</font> <a href="relset_1.html#K1" title="RELSET_1:func.1">\/</a> <font color="Maroon" title="c19">b12</font> is   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c20">c2</font> = <font color="Maroon" title="c15">b'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c16">b1'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="partfun1.html#K4" title="PARTFUN1:func.4">PFuncs</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">C</font> <b>by </b><i><a class="ref" href="partfun1.html#T119" title="PARTFUN1:th.119">PARTFUN1:119</a></i>;<br/><a NAME="E23:31_1_1"/><i><font color="Green" title="E37">A15</font></i>: 
<font color="Maroon" title="c20">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font>
 <b>by </b><i><a class="txt" href="substlat.html#E3:31_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="substlat.html#E10:31_1_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="substlat.html#E18:31_1_1"><i><font color="Green" title="E35">A13</font></i></a></i>;<br/><a NAME="E24:31_1_1"/>
<font color="Maroon" title="c14">c1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="txt" href="substlat.html#E12:31_1_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><a NAME="E25:31_1_1"/><b>then </b><i><font color="Green" title="E38">A16</font></i>: 
<font color="Maroon" title="c14">c1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="txt" href="substlat.html#E15:31_1_1"><i><font color="Green" title="E33">A11</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E26:31_1_1"/>
<font color="Maroon" title="c20">c2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">b</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c11">c</font>
 <b>by </b><i><a class="txt" href="substlat.html#E15:31_1_1"><i><font color="Green" title="E33">A11</font></i></a>, <a class="txt" href="substlat.html#E17:31_1_1"><i><font color="Green" title="E34">A12</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><a NAME="E27:31_1_1"/><b>then </b>
<font color="Maroon" title="c20">c2</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c17">c1'</font>
 <b>by </b><i><a class="txt" href="substlat.html#E5:31_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="substlat.html#E8:31_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="txt" href="substlat.html#E25:31_1_1"><i><font color="Green" title="E38">A16</font></i></a>, <a class="ref" href="partfun1.html#T139" title="PARTFUN1:th.139">PARTFUN1:139</a></i>;<br/><b>hence </b><a NAME="E28:31_1_1"/>
<font color="Maroon" title="c9">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font>
 <b>by </b><i><a class="txt" href="substlat.html#E5:31_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="substlat.html#E11:31_1_1"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="substlat.html#E12:31_1_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="txt" href="substlat.html#E19:31_1_1"><i><font color="Green" title="E36">A14</font></i></a>, <a class="txt" href="substlat.html#E23:31_1_1"><i><font color="Green" title="E37">A15</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="E3:31_1"/>
<font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c7">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c8">M</font>
 <b>by </b><i><a class="txt" href="substlat.html#E11"><i><font color="Green" title="E8">Lm2</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>
<a NAME="E3:31"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> &amp; <font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font> )
 
<b>by </b><i><a class="txt" href="substlat.html#E1:31"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:31"/>
<font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">K</font> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="substlat.html#K4" title="SUBSTLAT:func.4">^</a> <font color="Maroon" title="c5">M</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
