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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</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>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> holds <br/>for <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>  ex <font color="Olive" title="b4">x</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b4">x</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font></span><br/><b>let </b><font color="Maroon" title="c2">a</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">a</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="c1">F</font> implies for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>  ex <font color="Olive" title="b3">x</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">c</font> )</span><br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c2">a</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="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font>  ex <font color="Olive" title="b3">x</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b3">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">c</font></span><br/>

<b>let </b><font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being  <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font></span><br/>



<b>consider </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">z</font> being   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <font color="Maroon" title="c1">F</font><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green" title="E14">A2</font></i>: 
(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span>,<font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="#E1:25"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">x</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font></span><br/>

<b>thus </b><a NAME="E4:25"/>
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="txt" href="#E3:25"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="algstr_3.html#D7" target="_self" title="ALGSTR_3:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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