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Revision as of 15:20, 7 February 2009
, 15:20, 7 February 2009→Derived Equivalence Relations: mathematical markup
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By applying the form of Fact 1 to the special case where X = Den(R, x) and Y = Den(R, y), one obtains the following facts.
−
# If <math>L\!</math> is a sign relation such that <math>\operatorname{Con}(L)</math> is a SER on <math>S = I,\!</math> then <math>[x]_L\!</math> is the SEC of <math>x\!</math> under <math>\operatorname{Con}(L).</math>
# If <math>L\!</math> is a sign relation such that <math>\operatorname{Con}(L)</math> is a SER on <math>S = I,\!</math> then <math>[x]_L\!</math> is the SEC of <math>x\!</math> under <math>\operatorname{Con}(L).</math>
# If <math>L\!</math> is a sign relation such that <math>\operatorname{Der}(L)</math> is a DER on <math>S = I,\!</math> then <math>[x]^L\!</math> is the DEC of <math>x\!</math> under <math>\operatorname{Der}(L).</math>
# If <math>L\!</math> is a sign relation such that <math>\operatorname{Der}(L)</math> is a DER on <math>S = I,\!</math> then <math>[x]^L\!</math> is the DEC of <math>x\!</math> under <math>\operatorname{Der}(L).</math>
+
+By applying the form of Fact 1 to the special case where <math>X = \operatorname{Den}(L, x)</math> and <math>Y = \operatorname{Den}(L, y),</math> one obtains the following facts.
+
+<br>
<pre>
<pre>
−Fact 2.1
Fact 2.1
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(( {ROS.x} , {ROS.y} ))$(o)
(( {ROS.x} , {ROS.y} ))$(o)
} :D12a
} :D12a
+</pre>
+<br>
+<pre>
Fact 2.2
Fact 2.2
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))$(o)
))$(o)
} :$
} :$
+</pre>
+<br>
+<pre>
Fact 2.3
Fact 2.3
