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<b>let </b><font color="Maroon" title="c12">a</font>, <font color="Maroon" title="c13">b</font>, <font color="Maroon" title="c14">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c10">dL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c14">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c13">b</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="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c14">d</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c14">d</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</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="c14">d</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font></span>)</span> )</span><br/>

<a NAME="E1:15"/><i><font color="Green" title="E26">A1</font></i>: 
( ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,2 ) or ( <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c13">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 &amp; <font color="Maroon" title="c14">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,2 ) )
 
<b>by </b><i><a class="txt" href="realset2.html#E11"><i><font color="Green" title="E2">Lm2</font></i></a>, <a class="ref" href="card_1.html#T88" title="CARD_1:th.88">CARD_1:88</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:15"/>
<font color="Maroon" title="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c14">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c13">b</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="c12">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c14">d</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E17"><i><font color="Green" title="E6">Lm6</font></i></a>, <a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a>, <a class="txt" href="realset2.html#E20"><i><font color="Green" title="E9">Lm9</font></i></a>, <a class="txt" href="realset2.html#E24"><i><font color="Green" title="E13">Lm13</font></i></a>, <a class="txt" href="realset2.html#E25"><i><font color="Green" title="E14">Lm14</font></i></a>, <a class="txt" href="realset2.html#E26"><i><font color="Green" title="E15">Lm15</font></i></a>, <a class="txt" href="realset2.html#E27"><i><font color="Green" title="E16">Lm16</font></i></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="c13">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c14">d</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</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="c14">d</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font></span>)</span></span><br/>

<b>thus </b><a NAME="E3:15"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c14">d</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</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="c14">d</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c12">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="realset2.html#E1:15"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="realset2.html#E17"><i><font color="Green" title="E6">Lm6</font></i></a>, <a class="txt" href="realset2.html#E18"><i><font color="Green" title="E7">Lm7</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green" title="E8">Lm8</font></i></a>, <a class="txt" href="realset2.html#E20"><i><font color="Green" title="E9">Lm9</font></i></a>, <a class="txt" href="realset2.html#E24"><i><font color="Green" title="E13">Lm13</font></i></a>, <a class="txt" href="realset2.html#E25"><i><font color="Green" title="E14">Lm14</font></i></a>, <a class="txt" href="realset2.html#E26"><i><font color="Green" title="E15">Lm15</font></i></a>, <a class="txt" href="realset2.html#E27"><i><font color="Green" title="E16">Lm16</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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