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<span class="kw">let </span><font color="Maroon" title="c1">D</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">  <a href="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font> is  <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K4" title="RFUNCT_3:func.4">PFuncs</a> <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="binop_1.html#D13" title="BINOP_1:def.13">BINOP_1:def 13</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="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">F1</font>,<font color="Maroon" title="c3">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">F2</font>,<font color="Maroon" title="c2">F1</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">o</font> =  <a href="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">F1</font>,<font color="Maroon" title="c3">F2</font> = 
<font color="Maroon" title="c3">F2</font> <a href="rfunct_3.html#K6" title="RFUNCT_3:func.6">+</a> <font color="Maroon" title="c2">F1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D4" target="_self" title="RFUNCT_3:def.4">Def4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfunct_3.html#K14" title="RFUNCT_3:func.14">addpfunc</a> <font color="Maroon" title="c1">D</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">F2</font>,<font color="Maroon" title="c2">F1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_3.html#D4" target="_self" title="RFUNCT_3:def.4">Def4</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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