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<span class="kw">let </span><font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c2">u9</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u9</font> implies  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">v9</font> being   <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>  ex <font color="Olive" title="b3">a</font> being   <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> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c1">u</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">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="c2">u9</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">v9</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:17"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c1">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">u9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">v9</font> being   <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>  ex <font color="Olive" title="b3">a</font> being   <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> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c1">u</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">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="c2">u9</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">v9</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">v9</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font> being   <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> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">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="c2">u9</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">v9</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">uu</font> = <font color="Maroon" title="c1">u</font>, <font color="Maroon" title="c6">uu9</font> = <font color="Maroon" title="c2">u9</font>, <font color="Maroon" title="c7">vv</font> = <font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c8">vv9</font> = <font color="Maroon" title="c4">v9</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">aa</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">uu</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">vv</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">uu9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">vv9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="algstr_3.html#T1" target="_self" title="ALGSTR_3:th.1">Th3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c9">aa</font> as   <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> ;<br/>
<a NAME="E6:17"/>
(  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c1">u</font>,<font color="Maroon" title="c10">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">uu</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">vv</font> &amp;  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c2">u9</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c4">v9</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">uu9</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c9">aa</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c8">vv9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algstr_3.html#D2" target="_self" title="ALGSTR_3:def.2">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:17"/>
 ex <font color="Olive" title="b1">a</font> being   <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> st  <a href="algstr_3.html#K1" title="ALGSTR_3:func.1">Tern</a> (<font color="Maroon" title="c1">u</font>,<font color="Olive" title="b1">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="c2">u9</font>,<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c4">v9</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E12">A2</font></span></a></span>; <a class="txt" 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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