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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="algstr_3.html#NM2" title="ALGSTR_3:NM.2">Ternary-Field</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">a</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font>, <font color="Olive" title="b5">u9</font>, <font color="Olive" title="b6">v9</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a9</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b5">u9</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b6">v9</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">u</font>,<font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b5">u9</font>,<font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">v9</font> holds <br/>( <font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">u9</font> &amp; <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">v9</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">a9</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">u9</font>, <font color="Maroon" title="c7">v9</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a9</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c6">u9</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">v9</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c6">u9</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">v9</font> implies ( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u9</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v9</font> ) )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a9</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c6">u9</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c7">v9</font>
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c6">u9</font>,<font color="Maroon" title="c3">a9</font>,<font color="Maroon" title="c7">v9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u9</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v9</font> )</span><br/>

<a NAME="E4:26"/>
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26"/>
( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u9</font> &amp; <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</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/>


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