(* Author: Mathias Fleury, MPII
Simprocs for multisets, based on Larry Paulson's simprocs for
natural numbers and numerals.
*)
signature MULTISET_SIMPROCS =
sig
val subset_cancel_msets: Proof.context -> cterm -> thm option
val subseteq_cancel_msets: Proof.context -> cterm -> thm option
end;
structure Multiset_Simprocs : MULTISET_SIMPROCS =
struct
structure Subset_Cancel_Multiset = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_binrel @{const_name subset_mset}
val dest_bal = HOLogic.dest_bin @{const_name subset_mset} dummyT
val bal_add1 = @{thm mset_subset_add_iff1[unfolded repeat_mset_iterate_add]} RS trans
val bal_add2 = @{thm mset_subset_add_iff2[unfolded repeat_mset_iterate_add]} RS trans
);
structure Subseteq_Cancel_Multiset = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_binrel @{const_name subseteq_mset}
val dest_bal = HOLogic.dest_bin @{const_name subseteq_mset} dummyT
val bal_add1 = @{thm mset_subseteq_add_iff1[unfolded repeat_mset_iterate_add]} RS trans
val bal_add2 = @{thm mset_subseteq_add_iff2[unfolded repeat_mset_iterate_add]} RS trans
);
val subset_cancel_msets = Subset_Cancel_Multiset.proc;
val subseteq_cancel_msets = Subseteq_Cancel_Multiset.proc;
end