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<b>let </b><font color="Maroon" title="c4">Q1</font>, <font color="Maroon" title="c5">Q2</font> be   <a href="msualg_6.html#NM4" title="MSUALG_6:NM.4">EquationalTheory</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Q1</font> &amp; ( for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#NM4" title="MSUALG_6:NM.4">EquationalTheory</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c4">Q1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> ) &amp; <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">Q2</font> &amp; ( for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#NM4" title="MSUALG_6:NM.4">EquationalTheory</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c5">Q2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> ) implies <font color="Maroon" title="c4">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:81_1_1"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Q1</font>
 <b>and </b><br/><a NAME="E2:81_1_1"/><i><font color="Green" title="E56">A2</font></i>: 
for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#NM4" title="MSUALG_6:NM.4">EquationalTheory</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c4">Q1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font>
 <b>and </b><br/><a NAME="E3:81_1_1"/><i><font color="Green" title="E57">A3</font></i>: 
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">Q2</font>
 <b>and </b><br/><a NAME="E4:81_1_1"/><i><font color="Green" title="E58">A4</font></i>: 
for <font color="Olive" title="b1">Q</font> being  <a href="msualg_6.html#NM4" title="MSUALG_6:NM.4">EquationalTheory</a> of <font color="Maroon" title="c2">A</font>  st <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font> holds <br/><font color="Maroon" title="c5">Q2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b1">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q2</font></span><br/>

<b>thus </b><a NAME="E5:81_1_1"/>
( <font color="Maroon" title="c4">Q1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">Q2</font> &amp; <font color="Maroon" title="c5">Q2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Q1</font> )
 <b>by </b><i><a class="txt" href="msualg_6.html#E1:81_1_1"><i><font color="Green" title="E55">A1</font></i></a>, <a class="txt" href="msualg_6.html#E2:81_1_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="txt" href="msualg_6.html#E3:81_1_1"><i><font color="Green" title="E57">A3</font></i></a>, <a class="txt" href="msualg_6.html#E4:81_1_1"><i><font color="Green" title="E58">A4</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a> <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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