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<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ,   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ) <span class="kw">-&gt; </span>   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  = <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> $1,$2;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span>)</span><span class="kw"> such that </span><br/><a NAME="E2:6_1_1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds  <font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">take </span>
<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"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds  <font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font></span><br/>

<span class="kw">thus </span><a NAME="E3:6_1_1"/>
<font color="Maroon" title="c2">F</font> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c4">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E2">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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