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<span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies <font color="Maroon" title="c2">F</font> is  <a href="rlaffin1.html#V2" title="RLAFFIN1:attr.2">affinely-independent</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:64_1_1"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">F</font> is  <a href="rlaffin1.html#V2" title="RLAFFIN1:attr.2">affinely-independent</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="rlaffin1.html#D5" target="_self" title="RLAFFIN1:def.5">RLAFFIN1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> implies <font color="Maroon" title="c3">A</font> is  <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:64_1_1"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">A</font> is  <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:64_1_1"/>
<font color="Maroon" title="c3">A</font> is  <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:64_1_1"><span class="lab"><font color="Green" title="E50">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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