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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font>,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font> =  <a href="zmodul02.html#K13" title="ZMODUL02:func.13">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> $1</span>)</span> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <span class="p2">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> $2</span>)</span></span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">o</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:33_1_1"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
 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="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">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>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" onmouseover="rs('binop_1/S4')" onmouseout="rh()">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">take </span>
<font color="Maroon" title="c3">o</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">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="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Olive" title="b1">e1</font></span>)</span> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <span class="p1">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Olive" title="b2">e2</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">e1</font>, <font color="Maroon" title="c5">e2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zmodul02.html#K11" title="ZMODUL02:func.11">LinComb</a> <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">e1</font>,<font color="Maroon" title="c5">e2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c4">e1</font></span>)</span> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <span class="p1">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c5">e2</font></span>)</span></span><br/>



<span class="kw">thus </span><font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">e1</font>,<font color="Maroon" title="c5">e2</font>) = 
 <a href="zmodul02.html#K13" title="ZMODUL02:func.13">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c4">e1</font></span>)</span> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <span class="p2">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c5">e2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:33_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c4">e1</font></span>)</span> <a href="vectsp_6.html#K5" title="VECTSP_6:func.5">+</a> <span class="p1">(<span class="default"><a href="zmodul02.html#K12" title="ZMODUL02:func.12">@</a> <font color="Maroon" title="c5">e2</font></span>)</span>

; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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