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(* Title: HOL/Library/Cancellation/cancel_simprocs.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Author: Mathias Fleury, MPII
Cancelation simprocs declaration.
*)
signature CANCEL_SIMPROCS =
sig
val eq_cancel: Proof.context -> cterm -> thm option
val less_cancel: Proof.context -> cterm -> thm option
val less_eq_cancel: Proof.context -> cterm -> thm option
val diff_cancel: Proof.context -> cterm -> thm option
end;
structure Cancel_Simprocs : CANCEL_SIMPROCS =
struct
structure Eq_Cancel_Comm_Monoid_add = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_eq
val dest_bal = HOLogic.dest_bin \<^const_name>\<open>HOL.eq\<close> dummyT
val bal_add1 = @{thm iterate_add_eq_add_iff1} RS trans
val bal_add2 = @{thm iterate_add_eq_add_iff2} RS trans
);
structure Eq_Cancel_Comm_Monoid_less = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_binrel \<^const_name>\<open>Orderings.less\<close>
val dest_bal = HOLogic.dest_bin \<^const_name>\<open>Orderings.less\<close> dummyT
val bal_add1 = @{thm iterate_add_less_iff1} RS trans
val bal_add2 = @{thm iterate_add_less_iff2} RS trans
);
structure Eq_Cancel_Comm_Monoid_less_eq = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_binrel \<^const_name>\<open>Orderings.less_eq\<close>
val dest_bal = HOLogic.dest_bin \<^const_name>\<open>Orderings.less_eq\<close> dummyT
val bal_add1 = @{thm iterate_add_less_eq_iff1} RS trans
val bal_add2 = @{thm iterate_add_less_eq_iff2} RS trans
);
structure Diff_Cancel_Comm_Monoid_less_eq = Cancel_Fun
(open Cancel_Data
val mk_bal = HOLogic.mk_binop \<^const_name>\<open>Groups.minus\<close>
val dest_bal = HOLogic.dest_bin \<^const_name>\<open>Groups.minus\<close> dummyT
val bal_add1 = @{thm iterate_add_add_eq1} RS trans
val bal_add2 = @{thm iterate_add_diff_add_eq2} RS trans
);
val eq_cancel = Eq_Cancel_Comm_Monoid_add.proc;
val less_cancel = Eq_Cancel_Comm_Monoid_less.proc;
val less_eq_cancel = Eq_Cancel_Comm_Monoid_less_eq.proc;
val diff_cancel = Diff_Cancel_Comm_Monoid_less_eq.proc;
end
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