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<div class="add">

<span class="kw">thus </span><a NAME="E1:7_1"/>
( <font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() implies <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()] )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()] implies <font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="7_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:7_1_1"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]</span><br/>

<a NAME="E2:7_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</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">a</font>] </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:7_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="lmod_7.html#S6" target="_self" onmouseover="rs('lmod_7/S6')" onmouseout="rh()">LMOD_7:sch 6</a>(<a class="txt" href="#E2:7_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>);</span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:7_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()</span><br/>

<span class="kw">hence </span><a NAME="E3:7_1"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:7"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
