@@ -21,26 +21,26 @@ module LEMMAS-NO-SMT-SPEC
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// Arithmetic simplification
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// -------------------------
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- claim <k> runLemma ( 5 +Int X ) => doneLemma ( X +Int 5 ) ... </k>
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- claim <k> runLemma ( X -Int 5 ) => doneLemma ( X +Int (0 -Int 5) ) ... </k>
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- claim <k> runLemma ( (X +Int 3) +Int 5 ) => doneLemma ( X +Int 8 ) ... </k>
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- claim <k> runLemma ( 3 +Int (X +Int 5) ) => doneLemma ( X +Int 8 ) ... </k>
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- claim <k> runLemma ( 5 -Int (X +Int 3) ) => doneLemma ( 2 -Int X ) ... </k>
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- claim <k> runLemma ( 5 +Int (3 +Int X) ) => doneLemma ( 8 +Int X ) ... </k>
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- claim <k> runLemma ( 5 +Int (3 -Int X) ) => doneLemma ( 8 -Int X ) ... </k>
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- claim <k> runLemma ( (5 -Int X) +Int 3 ) => doneLemma ( 8 -Int X ) ... </k>
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- claim <k> runLemma ( 5 -Int (3 +Int X) ) => doneLemma ( 2 -Int X ) ... </k>
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- claim <k> runLemma ( 5 -Int (3 -Int X) ) => doneLemma ( 2 +Int X ) ... </k>
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- claim <k> runLemma ( (X -Int 5) -Int 3 ) => doneLemma ( X -Int 8 ) ... </k>
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- claim <k> runLemma ( 5 &Int (3 &Int X) ) => doneLemma ( 1 &Int X ) ... </k>
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+ claim [int-simpl-01]: <k> runLemma ( 5 +Int X ) => doneLemma ( X +Int 5 ) ... </k>
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+ claim [int-simpl-02]: <k> runLemma ( X -Int 5 ) => doneLemma ( X +Int (0 -Int 5) ) ... </k>
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+ claim [int-simpl-03]: <k> runLemma ( (X +Int 3) +Int 5 ) => doneLemma ( X +Int 8 ) ... </k>
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+ claim [int-simpl-04]: <k> runLemma ( 3 +Int (X +Int 5) ) => doneLemma ( X +Int 8 ) ... </k>
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+ claim [int-simpl-05]: <k> runLemma ( 5 -Int (X +Int 3) ) => doneLemma ( 2 -Int X ) ... </k>
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+ claim [int-simpl-06]: <k> runLemma ( 5 +Int (3 +Int X) ) => doneLemma ( 8 +Int X ) ... </k>
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+ claim [int-simpl-07]: <k> runLemma ( 5 +Int (3 -Int X) ) => doneLemma ( 8 -Int X ) ... </k>
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+ claim [int-simpl-08]: <k> runLemma ( (5 -Int X) +Int 3 ) => doneLemma ( 8 -Int X ) ... </k>
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+ claim [int-simpl-09]: <k> runLemma ( 5 -Int (3 +Int X) ) => doneLemma ( 2 -Int X ) ... </k>
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+ claim [int-simpl-10]: <k> runLemma ( 5 -Int (3 -Int X) ) => doneLemma ( 2 +Int X ) ... </k>
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+ claim [int-simpl-11]: <k> runLemma ( (X -Int 5) -Int 3 ) => doneLemma ( X -Int 8 ) ... </k>
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+ claim [int-simpl-12]: <k> runLemma ( 5 &Int (3 &Int X) ) => doneLemma ( 1 &Int X ) ... </k>
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// Boolean simplification
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// ----------------------
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- claim <k> runLemma ( (B ==Bool false) ==Bool false ) => doneLemma ( B ) ... </k>
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+ claim [bool-simpl-01]: <k> runLemma ( (B ==Bool false) ==Bool false ) => doneLemma ( B ) ... </k>
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// Awaiting Haskell backend updates
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- claim <k> runLemma ( bool2Word( B:Bool ) ==Int 1 ) => doneLemma ( B ==K true ) ... </k>
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- claim <k> runLemma ( 1 ==Int bool2Word( B:Bool ) ) => doneLemma ( B ==K true ) ... </k>
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+ claim [bool-simpl-02]: <k> runLemma ( bool2Word( B:Bool ) ==Int 1 ) => doneLemma ( B ==K true ) ... </k>
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+ claim [bool-simpl-03]: <k> runLemma ( 1 ==Int bool2Word( B:Bool ) ) => doneLemma ( B ==K true ) ... </k>
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endmodule
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