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<b>let </b><font color="Maroon" title="c1">V</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</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">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><br/> for <font color="Olive" title="b2">L1</font>, <font color="Olive" title="b3">L2</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b2">L1</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b3">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Olive" title="b3">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</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">L1</font>, <font color="Olive" title="b2">L2</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">L1</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> &amp; <font color="Olive" title="b2">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Olive" title="b2">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font> be    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">L1</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> implies <font color="Maroon" title="c3">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c4">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> )</span><br/>







<b>assume </b><a NAME="E1:30"/>
( <font color="Maroon" title="c3">L1</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c4">L2</font> is    <a href="convex4.html#M2" title="CONVEX4:mode.2">C_Linear_Combination</a> of <font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E2:30"/><b>then </b>
(  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c3">L1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c4">L2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="ref" href="convex4.html#D4" target="_self" title="CONVEX4:def.4">Def3</a></i>;<br/>
<a NAME="E3:30"/><b>then </b>
( <span class="p1">(<span class="default"><a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <font color="Maroon" title="c4">L2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="convex4.html#T19" target="_self" title="CONVEX4:th.19">Th58</a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E4:30"/>
 <a href="convex4.html#K1" title="CONVEX4:func.1">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="convex4.html#D4" target="_self" title="CONVEX4:def.4">CONVEX4:def 4</a> <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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