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<span class="kw">set </span><font color="Maroon" title="c2">R</font> =  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a> is  <a href="pencil_1.html#V15" title="PENCIL_1:attr.15">PLS-yielding</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pencil_1.html#D19" target="_self" title="PENCIL_1:def.19">PENCIL_1:def 19</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a></span>)</span> implies <font color="Maroon" title="c3">v</font> is   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:30_1_1"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">v</font> is   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a></span><br/>

<a NAME="E2:30_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:30_1_1"/>
<font color="Maroon" title="c3">v</font> is   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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