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<b>let </b><font color="Maroon" title="c1">st1</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="c1">st1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>) where <font color="Olive" title="b1">s1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">t1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>] </span>}</span>  implies <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c1">st1</font>] )</span><br/>

<b>assume </b><a NAME="E1:15_1"/>
<font color="Maroon" title="c1">st1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>) where <font color="Olive" title="b1">s1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">t1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</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">P<sub>2</sub></font>[<font color="Maroon" title="c1">st1</font>]</span><br/>

<a NAME="E2:15_1"/><b>then </b>
 ex <font color="Olive" title="b1">s1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() ex <font color="Olive" title="b2">t1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() st <br/>( <font color="Maroon" title="c1">st1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>] )
 
;<br/>
<b>hence </b><a NAME="E3:15_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c1">st1</font>]
 <b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E4">A1</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/>


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