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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font>,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> =  <a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> $1</span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p2">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> $2</span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c2">o</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font><b> such that </b><br/><a NAME="E2:55_1_1"/><i><font color="Green" title="E35">A1</font></i>: 
for <font color="Olive" title="b1">e1</font>, <font color="Olive" title="b2">e2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c2">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">e1</font>,<font color="Olive" title="b2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">e1</font>,<font color="Olive" title="b2">e2</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c2">o</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">e1</font>, <font color="Olive" title="b2">e2</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c2">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">e1</font>,<font color="Olive" title="b2">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Olive" title="b1">e1</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Olive" title="b2">e2</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c3">e1</font>, <font color="Maroon" title="c4">e2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="convex4.html#K10" title="CONVEX4:func.10">C_LinComb</a> <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="c2">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c4">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c3">e1</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c4">e2</font></span>)</span></span><br/>



<b>thus </b><font color="Maroon" title="c2">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">e1</font>,<font color="Maroon" title="c4">e2</font> = 
 <a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c3">e1</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p2">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c4">e2</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:55_1_1"><i><font color="Green" title="E35">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c3">e1</font></span>)</span> <a href="convex4.html#K5" title="CONVEX4:func.5">+</a> <span class="p1">(<span class="default"><a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <font color="Maroon" title="c4">e2</font></span>)</span>

; <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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