--- a/src/HOL/Numeral_Simprocs.thy Wed Nov 09 10:58:08 2011 +0100
+++ b/src/HOL/Numeral_Simprocs.thy Wed Nov 09 11:44:42 2011 +0100
@@ -202,6 +202,30 @@
use "Tools/nat_numeral_simprocs.ML"
+simproc_setup nateq_cancel_numerals
+ ("(l::nat) + m = n" | "(l::nat) = m + n" |
+ "(l::nat) * m = n" | "(l::nat) = m * n" |
+ "Suc m = n" | "m = Suc n") =
+ {* fn phi => Nat_Numeral_Simprocs.eq_cancel_numerals *}
+
+simproc_setup natless_cancel_numerals
+ ("(l::nat) + m < n" | "(l::nat) < m + n" |
+ "(l::nat) * m < n" | "(l::nat) < m * n" |
+ "Suc m < n" | "m < Suc n") =
+ {* fn phi => Nat_Numeral_Simprocs.less_cancel_numerals *}
+
+simproc_setup natle_cancel_numerals
+ ("(l::nat) + m \<le> n" | "(l::nat) \<le> m + n" |
+ "(l::nat) * m \<le> n" | "(l::nat) \<le> m * n" |
+ "Suc m \<le> n" | "m \<le> Suc n") =
+ {* fn phi => Nat_Numeral_Simprocs.le_cancel_numerals *}
+
+simproc_setup natdiff_cancel_numerals
+ ("((l::nat) + m) - n" | "(l::nat) - (m + n)" |
+ "(l::nat) * m - n" | "(l::nat) - m * n" |
+ "Suc m - n" | "m - Suc n") =
+ {* fn phi => Nat_Numeral_Simprocs.diff_cancel_numerals *}
+
declaration {*
K (Lin_Arith.add_simps (@{thms neg_simps} @ [@{thm Suc_nat_number_of}, @{thm int_nat_number_of}])
#> Lin_Arith.add_simps (@{thms ring_distribs} @ [@{thm Let_number_of}, @{thm Let_0}, @{thm Let_1},
@@ -222,7 +246,12 @@
@{simproc inteq_cancel_numerals},
@{simproc intless_cancel_numerals},
@{simproc intle_cancel_numerals}]
- #> Lin_Arith.add_simprocs (Nat_Numeral_Simprocs.combine_numerals :: Nat_Numeral_Simprocs.cancel_numerals))
+ #> Lin_Arith.add_simprocs
+ [Nat_Numeral_Simprocs.combine_numerals,
+ @{simproc nateq_cancel_numerals},
+ @{simproc natless_cancel_numerals},
+ @{simproc natle_cancel_numerals},
+ @{simproc natdiff_cancel_numerals}])
*}
end