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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">D</font> being 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> <br/> for <font color="Olive" title="b2">o</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">D</font><br/> for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font>, <font color="Olive" title="b5">h</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b1">D</font>  st <font color="Olive" title="b2">o</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> holds <br/><font color="Olive" title="b2">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g</font></span>)</span>,<font color="Olive" title="b5">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b3">f</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b4">g</font>,<font color="Olive" title="b5">h</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font> being  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">D</font><br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">h</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">D</font>  st <font color="Olive" title="b1">o</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> holds <br/><font color="Olive" title="b1">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span>,<font color="Olive" title="b4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b2">f</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b4">h</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">o</font> be   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">D</font>  st <font color="Maroon" title="c3">o</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> holds <br/><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span>,<font color="Olive" title="b3">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Olive" title="b2">g</font>,<font color="Olive" title="b3">h</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c6">h</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">o</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> implies <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span> )</span><br/>











<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E4">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font> holds  <font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span>,<font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D14" title="BINOP_1:def.14">BINOP_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span></span><br/>

<a NAME="E2:15"/><i><font color="Green" title="E5">A2</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">D</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> )</span><br/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span><br/><a NAME="E2:15_1"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">g</font> &amp; <font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">h</font> )
 <b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c9">b</font> = <font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c10">c</font> = <font color="Maroon" title="c6">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">D</font> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font> = 
<font color="Maroon" title="c3">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>,<font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="monoid_1.html#E1:15_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span>)</span>,<font color="Maroon" title="c10">c</font>
<b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="monoid_1.html#E1:15_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c8">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font></span>)</span>
<b>by </b><i><a class="txt" href="monoid_1.html#E1:15"><i><font color="Green" title="E4">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">o</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font></span>)</span>
<b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="monoid_1.html#E1:15_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="monoid_1.html#E1:15_1"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="funcop_1.html#T28" title="FUNCOP_1:th.28">FUNCOP_1:28</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15"/>
<font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c6">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">o</font> <a href="monoid_1.html#K3" title="MONOID_1:func.3">.:</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c6">h</font></span>)</span>
 <b>by </b><i><a class="txt" href="monoid_1.html#E2:15"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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