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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">E</font> being   <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">K</font> being  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b3">BE</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b4">BK</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">E</font>)</span>)</span><br/>  for <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">a2</font>, <font color="Olive" title="b7">b1</font>, <font color="Olive" title="b8">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">K</font>  st <font color="Olive" title="b5">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">BE</font> &amp; <font color="Olive" title="b6">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">BE</font> &amp; <font color="Olive" title="b7">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">BK</font> &amp; <font color="Olive" title="b8">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">BK</font> &amp; <font color="Olive" title="b5">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b8">b2</font> holds <br/>( <font color="Olive" title="b5">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a2</font> &amp; <font color="Olive" title="b7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">b2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be   <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</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">K</font> being  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">BE</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b3">BK</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font>  st <font color="Olive" title="b4">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">BE</font> &amp; <font color="Olive" title="b5">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">BE</font> &amp; <font color="Olive" title="b6">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">BK</font> &amp; <font color="Olive" title="b7">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">BK</font> &amp; <font color="Olive" title="b4">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b7">b2</font> holds <br/>( <font color="Olive" title="b4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a2</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">b2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</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">BE</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b2">BK</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">a2</font>, <font color="Olive" title="b5">b1</font>, <font color="Olive" title="b6">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font>  st <font color="Olive" title="b3">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">BE</font> &amp; <font color="Olive" title="b4">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">BE</font> &amp; <font color="Olive" title="b5">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">BK</font> &amp; <font color="Olive" title="b6">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">BK</font> &amp; <font color="Olive" title="b3">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b5">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b6">b2</font> holds <br/>( <font color="Olive" title="b3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">a2</font> &amp; <font color="Olive" title="b5">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">b2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">BE</font> be   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</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">  for <font color="Olive" title="b1">BK</font> being   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font>  st <font color="Olive" title="b2">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Olive" title="b3">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Olive" title="b4">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">BK</font> &amp; <font color="Olive" title="b5">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">BK</font> &amp; <font color="Olive" title="b2">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b5">b2</font> holds <br/>( <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a2</font> &amp; <font color="Olive" title="b4">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">b2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">BK</font> be   <a href="vectsp_7.html#V1" title="VECTSP_7:attr.1">linearly-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</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">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">b2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font>  st <font color="Olive" title="b1">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Olive" title="b2">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Olive" title="b3">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> &amp; <font color="Olive" title="b4">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> &amp; <font color="Olive" title="b1">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">b2</font> holds <br/>( <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Olive" title="b3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">a2</font>, <font color="Maroon" title="c8">b1</font>, <font color="Maroon" title="c9">b2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</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="c6">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Maroon" title="c7">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> &amp; <font color="Maroon" title="c9">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> &amp; <font color="Maroon" title="c6">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">b2</font> implies ( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
( <font color="Maroon" title="c6">a1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Maroon" title="c7">a2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> &amp; <font color="Maroon" title="c9">b2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</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"> (  not <font color="Maroon" title="c6">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">b2</font> or ( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> ) )</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">b1v</font> = <font color="Maroon" title="c8">b1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span> ;<br/>
<span class="kw">assume </span><a NAME="E3:50"/><span class="lab"><font color="Green" title="E24">A2</font></span>: 
<font color="Maroon" title="c6">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c9">b2</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="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> )</span><br/>

<a NAME="E4:50"/>
<span class="p1"><a href="field_7.html#K2" title="FIELD_7:func.2">{</a><span class="default"><font color="Maroon" title="c10">b1v</font></span><a href="field_7.html#K2" title="FIELD_7:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">BK</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:50"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_7.html#T1" onmouseover="rs('vectsp_7/T1')" onmouseout="rh()">VECTSP_7:1</a>, <a class="ref" href="vectsp_7.html#T3" onmouseover="rs('vectsp_7/T3')" onmouseout="rh()">VECTSP_7:3</a></span>;<br/>
<a NAME="E6:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A3</font></span>: 
<font color="Maroon" title="c8">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D6" onmouseover="rs('field_4/D6')" onmouseout="rh()">FIELD_4:def 6</a></span>;<br/>
<a NAME="E7:50"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
<font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="field_7.html#E29"><span class="lab"><font color="Green" title="E22">BE0</font></span></a></span>;<br/>
<a NAME="E8:50"/>
<font color="Maroon" title="c6">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="ref" href="group_1.html#D12" onmouseover="rs('group_1/D12')" onmouseout="rh()">GROUP_1:def 12</a></span>;<br/>
<a NAME="E9:50"/><span class="kw">then </span>
<font color="Maroon" title="c8">b1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c7">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D12" onmouseover="rs('group_1/D12')" onmouseout="rh()">GROUP_1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:50"/>
( <font color="Maroon" title="c6">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">a2</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="ref" href="vectsp_2.html#T8" onmouseover="rs('vectsp_2/T8')" onmouseout="rh()">VECTSP_2:8</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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