<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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>, <font color="Olive" title="b3">h</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  <span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b3">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span>,<font color="Olive" title="b3">h</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font>, <font color="Maroon" title="c4">h</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"> <span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c4">h</font></span><br/>



<span class="kw">thus </span><span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c3">g</font>,<font color="Maroon" title="c4">h</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><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">g</font>,<font color="Maroon" title="c4">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcsdom.html#D3" target="_self" title="FUNCSDOM:def.3">Def3</a></span>
<br/>.= 
<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="c2">f</font>,<span class="p1">(<span class="default"><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">g</font>,<font color="Maroon" title="c4">h</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcsdom.html#D3" target="_self" title="FUNCSDOM:def.3">Def3</a></span>
<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="funcsdom.html#K3" title="FUNCSDOM:func.3">.:</a> <span class="p1">(<span class="default"><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="c2">f</font>,<font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c4">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T76" title="FUNCOP_1:th.76">FUNCOP_1:76</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <span class="p1">(<span class="default"><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="c2">f</font>,<font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c4">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcsdom.html#D3" target="_self" title="FUNCSDOM:def.3">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funcsdom.html#K6" title="FUNCSDOM:func.6">RealFuncMult</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funcsdom.html#K1" title="FUNCSDOM:func.1">.</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">g</font></span>)</span>,<font color="Maroon" title="c4">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcsdom.html#D3" target="_self" title="FUNCSDOM:def.3">Def3</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/>


</div>
