<?xml version="1.0"?>
<div class="add">

<span class="kw">thus </span><a NAME="E1:22_1_1"/>
( <font color="Maroon" title="c1">F</font> is  <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a>  implies  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pencil_1.html#D13" target="_self" title="PENCIL_1:def.13">Def13</a>, <a class="ref" href="pencil_1.html#D14" target="_self" title="PENCIL_1:def.14">Def14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  ) implies <font color="Maroon" title="c1">F</font> is  <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:22_1_1"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is   non  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</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">F</font> is  <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">S</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pencil_1.html#D14" target="_self" title="PENCIL_1:def.14">PENCIL_1:def 14</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="c2">S</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> <font color="Maroon" title="c1">F</font> implies  not <font color="Maroon" title="c2">S</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:22_1_1"/>
( <font color="Maroon" title="c2">S</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> <font color="Maroon" title="c1">F</font> implies  not <font color="Maroon" title="c2">S</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E21">A1</font></span></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/>


</div>
