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<b>set </b><font color="Maroon" title="c1">F</font> =  <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c2">a</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> , <font color="Maroon" title="c3">b</font> =  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c6">z</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/><b>thus </b><a NAME="E1:56_1"/>
( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c7">X</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c8">Y</font> = <font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c9">Z</font> = <font color="Maroon" title="c6">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> ;<br/>
<b>thus </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c8">Y</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c7">X</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">X</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c8">Y</font></span>)</span> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c9">Z</font>
<b>by </b><i><a class="ref" href="mod_2.html#T34" target="_self" title="MOD_2:th.34">Th34</a></i>
<br/>.= 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c9">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T34" target="_self" title="MOD_2:th.34">Th34</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<a NAME="E5:56_1_1"/>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K10" title="MOD_2:func.10">-</a> <font color="Maroon" title="c7">X</font>
 
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">x</font></span>)</span> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <span class="p1">(<span class="default"><a href="mod_2.html#K10" title="MOD_2:func.10">-</a> <font color="Maroon" title="c7">X</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> 
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c8">Y</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c7">X</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c8">Y</font></span>)</span> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c9">Z</font>
<b>by </b><i><a class="ref" href="mod_2.html#T34" target="_self" title="MOD_2:th.34">Th34</a></i>
<br/>.= 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c9">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T34" target="_self" title="MOD_2:th.34">Th34</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">x</font> = 
<font color="Maroon" title="c3">b</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c7">X</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> &amp; ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span>)</span> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c7">X</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ) &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><br/>

<b>thus </b><a NAME="E11:56_1_1"/>
( <font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  implies  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:56_1_1_9"/>
<font color="Maroon" title="c4">x</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> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  st <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c10">Y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1,2</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span><b> such that </b><br/><a NAME="E3:56_1_1_9"/><i><font color="Green" title="E43">A1</font></i>: 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c10">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">y</font> = <font color="Maroon" title="c10">Y</font> as   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c11">y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> </span><br/>

<b>thus </b><a NAME="E5:56_1_1_9"/>
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> 
 <b>by </b><i><a class="txt" href="#E3:56_1_1_9"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E12:56_1_1"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span></span><br/>

<a NAME="E13:56_1_1"/><i><font color="Green" title="E43">A2</font></i>: 
( <font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c9">Z</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c8">Y</font> &amp; <font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c9">Z</font> )
 
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">z</font></span>)</span> = 
<font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">Y</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c9">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c8">Y</font></span>)</span> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">X</font> <a href="mod_2.html#K12" title="MOD_2:func.12">*</a> <font color="Maroon" title="c9">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#T35" target="_self" title="MOD_2:th.35">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c6">z</font></span>)</span>
<b>by </b><i><a class="txt" href="#E13:56_1_1"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="mod_2.html#T33" target="_self" title="MOD_2:th.33">Th33</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c4">F</font> =  <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  as   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> <b>by </b><i><a class="ref" href="mod_2.html#T36" target="_self" title="MOD_2:th.36">Th36</a></i>;<br/>
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c4">F</font></span>)</span> = 
<font color="Maroon" title="c3">b</font> <a href="mod_2.html#K11" title="MOD_2:func.11">+</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="mod_2.html#D18" target="_self" title="MOD_2:def.18">Def18</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="mod_2.html#D16" target="_self" title="MOD_2:def.16">Def16</a></i>
;<br/>
<b>hence </b><a NAME="E5:56"/>
 <a href="mod_2.html#K18" title="MOD_2:func.18">Z3</a>  is  <a href="vectsp_1.html#V9" title="VECTSP_1:attr.9">Fanoian</a> <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>
 <b>by </b><i><a class="ref" href="mod_2.html#T32" target="_self" title="MOD_2:th.32">Th32</a>, <a class="ref" href="vectsp_1.html#D29" title="VECTSP_1:def.29">VECTSP_1:def 29</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
