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

<span class="kw">set </span><font color="Maroon" title="c2">G</font> =  <a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">o</font> =  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>;<br/>
<span class="kw">thus </span><a NAME="E1:53_1_1"/>
 <a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font> is  <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</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="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="53_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c4">e</font> =  <a href="topgrp_1.html#K4" title="TOPGRP_1:func.4">id</a> <font color="Maroon" title="c1">T</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">e</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D2" onmouseover="rs('group_1/D2')" onmouseout="rh()">GROUP_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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c4">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  ex <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> ) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">h</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</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"> ( <font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> &amp; <font color="Maroon" title="c4">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> &amp;  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> st <br/>( <font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">h1</font> = <font color="Maroon" title="c5">h</font>, <font color="Maroon" title="c7">e1</font> = <font color="Maroon" title="c4">e</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">e</font> = 
<font color="Maroon" title="c7">e1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">h1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T17" onmouseover="rs('funct_2/T17')" onmouseout="rh()">FUNCT_2:17</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"> ( <font color="Maroon" title="c4">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> &amp;  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> st <br/>( <font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> ) )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c4">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> = 
<font color="Maroon" title="c6">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">e1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c5">h</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T17" onmouseover="rs('funct_2/T17')" onmouseout="rh()">FUNCT_2:17</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">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> st <br/>( <font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">h1</font> = <font color="Maroon" title="c5">h</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E6:53_1_1_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<a NAME="E7:53_1_1_1"/>
<font color="Maroon" title="c8">h1</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T30" target="_self" onmouseover="rs('topgrp_1/T30')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">g</font> = <font color="Maroon" title="c8">h1</font> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">g1</font> = <font color="Maroon" title="c9">g</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c9">g</font>
; <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"> ( <font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> &amp; <font color="Maroon" title="c9">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font> )</span><br/>

<a NAME="E10:53_1_1_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c8">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c5">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">g</font> = 
<font color="Maroon" title="c10">g1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">h1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c4">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:53_1_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="#E10:53_1_1_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="tops_2.html#T52" onmouseover="rs('tops_2/T52')" onmouseout="rh()">TOPS_2:52</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"> <font color="Maroon" title="c9">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">e</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c9">g</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">h</font> = 
<font color="Maroon" title="c8">h1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c10">g1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c4">e</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:53_1_1_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="tops_2.html#T52" onmouseover="rs('tops_2/T52')" onmouseout="rh()">TOPS_2:52</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="c4">x</font>, <font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c6">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_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"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c8">g</font> = <font color="Maroon" title="c5">y</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c8">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c10">r</font> = <font color="Maroon" title="c6">z</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a>, <a class="ref" href="topgrp_1.html#T31" target="_self" onmouseover="rs('topgrp_1/T31')" onmouseout="rh()">Th30</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c10">r</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">g</font> as    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">T</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T31" target="_self" onmouseover="rs('topgrp_1/T31')" onmouseout="rh()">Th30</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> = 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f</font></span>)</span>,<font color="Maroon" title="c6">z</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c10">r</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">p</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">r</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T36" onmouseover="rs('relat_1/T36')" onmouseout="rh()">RELAT_1:36</a></span>
<br/>.= 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="topgrp_1.html#K5" title="TOPGRP_1:func.5">HomeoGroup</a> <font color="Maroon" title="c1">T</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c11">a</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/D5')" onmouseout="rh()">Def5</a></span>
<br/>.= 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#D5" target="_self" onmouseover="rs('topgrp_1/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/>


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