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<b>let </b><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v'</font> be   <a href="algstr_3.html#NM1" title="ALGSTR_3:NM.1">Scalar</a> of <a href="algstr_3.html#K3" title="ALGSTR_3:func.3">TernaryFieldEx</a> ; <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="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">v'</font> implies <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v'</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c5">z</font> = <font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c6">x</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c7">y</font> = <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c8">y'</font> = <font color="Maroon" title="c4">v'</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E2:15"/><i><font color="Green" title="E9">A1</font></i>: 
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">y</font>
 
<b>by </b><i><a class="ref" href="algstr_3.html#D4" target="_self" title="ALGSTR_3:def.4">Def4</a></i>;<br/>
<a NAME="E3:15"/>
 <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">v'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c6">x</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">y'</font>
 
<b>by </b><i><a class="ref" href="algstr_3.html#D4" target="_self" title="ALGSTR_3:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E4:15"/>
(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> <font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">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="c1">u</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">v'</font> implies <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v'</font> )
 <b>by </b><i><a class="txt" href="#E2:15"><i><font color="Green" title="E9">A1</font></i></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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