<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">AFV</font> be   <a href="afvect0.html#NM1" title="AFVECT0:NM.1">WeakAffVect</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">o</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Olive" title="b1">o</font></span>)</span> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b4">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="afvect0.html#K5" title="AFVECT0:func.5">GroupVect</a> <font color="Maroon" title="c1">AFV</font>,<font color="Maroon" title="c2">o</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font></span>)</span></span><br/>









<span class="kw">reconsider </span><font color="Maroon" title="c6">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c7">b9</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c8">c9</font> = <font color="Maroon" title="c5">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c4">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">b</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">p9</font> = <font color="Maroon" title="c4">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c12">q9</font> = <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">x9</font> = <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font></span>)</span>, <font color="Maroon" title="c14">y9</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">x99</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFV</font><span class="kw"> such that </span><br/><a NAME="E5:70"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
<font color="Maroon" title="c13">x9</font>,<font color="Maroon" title="c11">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c15">x99</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E6:70"/>
<font color="Maroon" title="c13">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K2" title="AFVECT0:func.2">Padd</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c11">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>;<br/>
<a NAME="E7:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">p9</font>,<font color="Maroon" title="c13">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D5" target="_self" title="AFVECT0:def.5">Def5</a></span>;<br/>
<a NAME="E8:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A2</font></span>: 
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">x9</font>,<font color="Maroon" title="c11">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T8" target="_self" title="AFVECT0:th.8">Th8</a></span>;<br/>
<a NAME="E9:70"/>
<font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c15">x99</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">x9</font>,<font color="Maroon" title="c11">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></span>;<br/>
<a NAME="E10:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A3</font></span>: 
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c15">x99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:70"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E11:70"/>
<font color="Maroon" title="c12">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K2" title="AFVECT0:func.2">Padd</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c7">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>;<br/>
<a NAME="E12:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c12">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D5" target="_self" title="AFVECT0:def.5">Def5</a></span>;<br/>
<a NAME="E13:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c12">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E14:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c12">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></span>;<br/>
<a NAME="E15:70"/>
<font color="Maroon" title="c11">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K2" title="AFVECT0:func.2">Padd</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b9</font>,<font color="Maroon" title="c8">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>;<br/>
<a NAME="E16:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c11">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D5" target="_self" title="AFVECT0:def.5">Def5</a></span>;<br/>
<a NAME="E17:70"/><span class="kw">then </span>
<font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c11">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></span>;<br/>
<a NAME="E18:70"/><span class="kw">then </span>
<font color="Maroon" title="c6">a9</font>,<font color="Maroon" title="c12">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c11">p9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:70"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E19:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A5</font></span>: 
<font color="Maroon" title="c12">q9</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">p9</font>,<font color="Maroon" title="c15">x99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:70"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E20:70"/>
<font color="Maroon" title="c13">x9</font>,<font color="Maroon" title="c8">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">p9</font>,<font color="Maroon" title="c15">x99</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:70"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E21:70"/><span class="kw">then </span>
<font color="Maroon" title="c12">q9</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">x9</font>,<font color="Maroon" title="c8">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:70"><span class="lab"><font color="Green" title="E40">A5</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<a NAME="E22:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c12">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c13">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T8" target="_self" title="AFVECT0:th.8">Th8</a></span>;<br/>
<a NAME="E23:70"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A6</font></span>: 
<font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c13">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c12">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></span>;<br/>
<a NAME="E24:70"/>
<font color="Maroon" title="c14">y9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afvect0.html#K2" title="AFVECT0:func.2">Padd</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c12">q9</font>,<font color="Maroon" title="c8">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D7" target="_self" title="AFVECT0:def.7">Def7</a></span>;<br/>
<a NAME="E25:70"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c12">q9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c14">y9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#D5" target="_self" title="AFVECT0:def.5">Def5</a></span>;<br/>
<a NAME="E26:70"/><span class="kw">then </span>
<font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c14">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c12">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T4" target="_self" title="AFVECT0:th.4">Th4</a></span>;<br/>
<a NAME="E27:70"/><span class="kw">then </span>
<font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c14">y9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c9</font>,<font color="Maroon" title="c13">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:70"><span class="lab"><font color="Green" title="E41">A6</font></span></a>, <a class="ref" href="afvect0.html#D1" target="_self" title="AFVECT0:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E28:70"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afvect0.html#T5" target="_self" title="AFVECT0:th.5">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
