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

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</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" title="b1">B</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">M</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">M</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b1">B</font> holds <br/><font color="Olive" title="b1">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b2">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">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">  for <font color="Olive" title="b1">M</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">M</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">B</font> holds <br/><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Olive" title="b1">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b1">M</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">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="c3">M</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">I</font> = <font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">J</font> = (<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">g</font> =  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">f</font> =  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">X</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
<font color="Maroon" title="c3">M</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Maroon" title="c2">B</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="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span><br/>

<a NAME="E2:34"/><span class="lab"><font color="Green" title="E23">A2</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="34_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI: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"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:34_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></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="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E3:34_1"/><span class="lab"><font color="Green" title="E24">A3</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:34_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T13" target="_self" onmouseover="rs('group_6/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">b</font> = <font color="Maroon" title="c10">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/>
<a NAME="E6:34_1"/>
(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a>  <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="group_6.html#D1" target="_self" onmouseover="rs('group_6/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E7:34_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:34_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_1"><span class="lab"><font color="Green" title="E24">A3</font></span></a>, <a class="ref" href="group_6.html#T14" target="_self" onmouseover="rs('group_6/T14')" onmouseout="rh()">Th14</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>
<div><span class="lab"><font color="Green" title="E24">A4</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="34_2"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> holds <br/> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> implies  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:34_2"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></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">  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">y</font>, <font color="Maroon" title="c11">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:34_2"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c10">y</font>,<font color="Maroon" title="c11">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D1" onmouseover="rs('relat_1/D1')" onmouseout="rh()">RELAT_1:def 1</a></span>;<br/><a NAME="E4:34_2"/>
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_2"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E3:34_2"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E6:34_2"/><span class="lab"><font color="Green" title="E27">A7</font></span>: 
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:34_2"/><span class="lab"><font color="Green" title="E28">A8</font></span>: 
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T13" target="_self" onmouseover="rs('group_6/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E8:34_2"/>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_2"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E3:34_2"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E10:34_2"/><span class="lab"><font color="Green" title="E29">A9</font></span>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E11:34_2"/>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c13">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T13" target="_self" onmouseover="rs('group_6/T13')" onmouseout="rh()">Th13</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c14">W1</font> = <font color="Maroon" title="c10">y</font>, <font color="Maroon" title="c15">W2</font> = <font color="Maroon" title="c11">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_6.html#NK4" title="GROUP_6:NK.4">Cosets</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:34_2"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E6:34_2"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="ref" href="group_6.html#T14" target="_self" onmouseover="rs('group_6/T14')" onmouseout="rh()">Th14</a></span>;<br/><span class="lab"><font color="Green" title="E30">A10</font></span>:  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> = 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c14">W1</font>,<font color="Maroon" title="c15">W2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_2"><span class="lab"><font color="Green" title="E26">A6</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:34_2"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E7:34_2"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="ref" href="group_6.html#D3" target="_self" onmouseover="rs('group_6/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c12">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T11" onmouseover="rs('group_3/T11')" onmouseout="rh()">GROUP_3:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c12">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T45" onmouseover="rs('group_4/T45')" onmouseout="rh()">GROUP_4:45</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c12">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T76" onmouseover="rs('group_2/T76')" onmouseout="rh()">GROUP_2:76</a></span>
<br/>.= 
<font color="Maroon" title="c13">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c12">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T106" onmouseover="rs('group_2/T106')" onmouseout="rh()">GROUP_2:106</a></span>
<br/>.= 
<font color="Maroon" title="c13">a</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">b</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T117" onmouseover="rs('group_3/T117')" onmouseout="rh()">GROUP_3:117</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T105" onmouseover="rs('group_2/T105')" onmouseout="rh()">GROUP_2:105</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c12">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T42" onmouseover="rs('group_2/T42')" onmouseout="rh()">GROUP_2:42</a></span>;<br/><a NAME="E15:34_2"/><span class="lab"><font color="Green" title="E31">A11</font></span>: 
(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a>  <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E22">A1</font></span></a>, <a class="ref" href="group_6.html#D1" target="_self" onmouseover="rs('group_6/D1')" onmouseout="rh()">Def1</a></span>;<br/><a NAME="E16:34_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A12</font></span>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">a9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:34_2"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E17:34_2"/>
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:34_2"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E15:34_2"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">V1</font> = <font color="Maroon" title="c10">y</font>, <font color="Maroon" title="c19">V2</font> = <font color="Maroon" title="c11">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_6.html#NK4" title="GROUP_6:NK.4">Cosets</a> <font color="Maroon" title="c3">M</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:34_2"><span class="lab"><font color="Green" title="E32">A12</font></span></a>, <a class="ref" href="group_6.html#T14" target="_self" onmouseover="rs('group_6/T14')" onmouseout="rh()">Th14</a></span>;<br/><a NAME="E19:34_2"/><span class="lab"><font color="Green" title="E33">A13</font></span>: 
<font color="Maroon" title="c16">a9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T43" onmouseover="rs('group_2/T43')" onmouseout="rh()">GROUP_2:43</a></span>;<br/><a NAME="E20:34_2"/><span class="lab"><font color="Green" title="E34">A14</font></span>: 
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c17">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:34_2"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="txt" href="#E15:34_2"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</a></span>;<br/> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> = 
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c18">V1</font>,<font color="Maroon" title="c19">V2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_2"><span class="lab"><font color="Green" title="E26">A6</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c17">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:34_2"><span class="lab"><font color="Green" title="E32">A12</font></span></a>, <a class="txt" href="#E20:34_2"><span class="lab"><font color="Green" title="E34">A14</font></span></a>, <a class="ref" href="group_6.html#D3" target="_self" onmouseover="rs('group_6/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">a9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c17">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T11" onmouseover="rs('group_3/T11')" onmouseout="rh()">GROUP_3:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a9</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">M</font></span>)</span></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c17">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_4.html#T45" onmouseover="rs('group_4/T45')" onmouseout="rh()">GROUP_4:45</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="group_2.html#K5" title="GROUP_2:func.5">*</a> <font color="Maroon" title="c17">b9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T76" onmouseover="rs('group_2/T76')" onmouseout="rh()">GROUP_2:76</a></span>
<br/>.= 
<font color="Maroon" title="c16">a9</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="group_2.html#K14" title="GROUP_2:func.14">*</a> <font color="Maroon" title="c17">b9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T106" onmouseover="rs('group_2/T106')" onmouseout="rh()">GROUP_2:106</a></span>
<br/>.= 
<font color="Maroon" title="c16">a9</font> <a href="group_2.html#K4" title="GROUP_2:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">b9</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T117" onmouseover="rs('group_3/T117')" onmouseout="rh()">GROUP_3:117</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">a9</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c17">b9</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c3">M</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_2.html#T105" onmouseover="rs('group_2/T105')" onmouseout="rh()">GROUP_2:105</a></span>
;<br/><span class="kw">hence </span><a NAME="E22:34_2"/>
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:34_2"><span class="lab"><font color="Green" title="E30">A10</font></span></a>, <a class="txt" href="#E15:34_2"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="txt" href="#E19:34_2"><span class="lab"><font color="Green" title="E33">A13</font></span></a>, <a class="ref" href="group_6.html#T2" target="_self" onmouseover="rs('group_6/T2')" onmouseout="rh()">Th2</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>
<a NAME="E4:34"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E5:34"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p3">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a>, <a class="ref" href="zfmisc_1.html#T96" onmouseover="rs('zfmisc_1/T96')" onmouseout="rh()">ZFMISC_1:96</a></span>;<br/>
<a NAME="E6:34"/><span class="kw">then </span>
 the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font></span>)</span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p2">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="funct_1.html#T46" onmouseover="rs('funct_1/T46')" onmouseout="rh()">FUNCT_1:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:34"/>
<font color="Maroon" title="c2">B</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">M</font>) <a href="group_6.html#K1" title="GROUP_6:func.1">`*`</a></span>)</span> is    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="group_2.html#D5" onmouseover="rs('group_2/D5')" onmouseout="rh()">GROUP_2:def 5</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>
