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<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</font><br/> for <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st not <font color="Olive" title="b3">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><font color="Olive" title="b3">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> </span><br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b2">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/><font color="Olive" title="b2">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> </span><br/><b>let </b><font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  implies <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  )</span><br/>









<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E22">A1</font></i>: 
not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> </span><br/>

<a NAME="E2:27"/><b>then </b>
 ex <font color="Olive" title="b1">l</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font> st <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 
<b>by </b><i><a class="ref" href="symsp_1.html#D1" target="_self" title="SYMSP_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
<font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="symsp_1.html#D5" target="_self" title="SYMSP_1:def.5">Def5</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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