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

<span class="kw">set </span><font color="Maroon" title="c2">o</font> =  <a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="binop_1.html#D2" onmouseover="rs('binop_1/D2')" onmouseout="rh()">BINOP_1:def 2</a> <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">  <a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font> is  <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>); <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"> <span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c3">F1</font>)</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>) = 
<font color="Maroon" title="c4">F2</font> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <font color="Maroon" title="c3">F1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c3">F1</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></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/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font>, <font color="Maroon" title="c5">F3</font> be    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>); <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="binop_1.html#D3" onmouseover="rs('binop_1/D3')" onmouseout="rh()">BINOP_1:def 3</a> <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"> <span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">F1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">F3</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>)</span>)</span>,<font color="Maroon" title="c5">F3</font>)</span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c3">F1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">F3</font>)</span>)</span>) = 
<font color="Maroon" title="c3">F1</font> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">F2</font>,<font color="Maroon" title="c5">F3</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c3">F1</font> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F2</font> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <font color="Maroon" title="c5">F3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">F1</font> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <font color="Maroon" title="c4">F2</font></span>)</span> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <font color="Maroon" title="c5">F3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T8" onmouseover="rs('rfunct_1/T8')" onmouseout="rh()">RFUNCT_1:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>)</span>)</span> <a href="lpspacc1.html#K1" title="LPSPACC1:func.1">+</a> <font color="Maroon" title="c5">F3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K9" title="LPSPACC1:func.9">addcpfunc</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c3">F1</font>,<font color="Maroon" title="c4">F2</font>)</span>)</span>,<font color="Maroon" title="c5">F3</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D5" target="_self" onmouseover="rs('lpspacc1/D5')" onmouseout="rh()">Def5</a></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/>


</div>
