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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
( ( <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 ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="realset2.html#E12"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a>, <a class="txt" href="realset2.html#E13"><span class="lab"><font color="Green" title="E4">Lm4</font></span></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></span>;<br/>
<span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="realset2.html#E19"><span class="lab"><font color="Green" title="E8">Lm8</font></span></a>, <a class="txt" href="realset2.html#E20"><span class="lab"><font color="Green" title="E9">Lm9</font></span></a>, <a class="txt" href="realset2.html#E21"><span class="lab"><font color="Green" title="E10">Lm10</font></span></a>, <a class="txt" href="realset2.html#E22"><span class="lab"><font color="Green" title="E11">Lm11</font></span></a>, <a class="txt" href="realset2.html#E26"><span class="lab"><font color="Green" title="E15">Lm15</font></span></a>, <a class="txt" href="realset2.html#E27"><span class="lab"><font color="Green" title="E16">Lm16</font></span></a>, <a class="txt" href="realset2.html#E28"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a>, <a class="txt" href="realset2.html#E29"><span class="lab"><font color="Green" title="E18">Lm18</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="realset2.html#E19"><span class="lab"><font color="Green" title="E8">Lm8</font></span></a>, <a class="txt" href="realset2.html#E20"><span class="lab"><font color="Green" title="E9">Lm9</font></span></a>, <a class="txt" href="realset2.html#E21"><span class="lab"><font color="Green" title="E10">Lm10</font></span></a>, <a class="txt" href="realset2.html#E22"><span class="lab"><font color="Green" title="E11">Lm11</font></span></a>, <a class="txt" href="realset2.html#E26"><span class="lab"><font color="Green" title="E15">Lm15</font></span></a>, <a class="txt" href="realset2.html#E27"><span class="lab"><font color="Green" title="E16">Lm16</font></span></a>, <a class="txt" href="realset2.html#E28"><span class="lab"><font color="Green" title="E17">Lm17</font></span></a>, <a class="txt" href="realset2.html#E29"><span class="lab"><font color="Green" title="E18">Lm18</font></span></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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