81 lines
2.7 KiB
Coq
81 lines
2.7 KiB
Coq
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Require Export Coq.Bool.Bool.
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Require Export Coq.Arith.Arith.
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Require Export Coq.Arith.EqNat.
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Require Export Coq.omega.Omega.
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Require Export Coq.Lists.List.
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Require Export Coq.ZArith.ZArith.
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Require Export Coq.Numbers.Natural.Peano.NPeano.
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Require Export Coq.Setoids.Setoid.
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Require Export Coq.Program.Equality. (**r Necessary for 'dependent induction'. *)
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Require Export LibTactics.
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Ltac autoinjection :=
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repeat match goal with
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| h: ?f _ = ?f _ |- _ => injection h; intros; clear h; subst
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| h: ?f _ _ = ?f _ _ |- _ => injection h; intros; clear h; subst
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| h: ?f _ _ _ = ?f _ _ _ |- _ => injection h; intros; clear h; subst
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| h: ?f _ _ _ _ = ?f _ _ _ _ |- _ => injection h; intros; clear h; subst
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| h: ?f _ _ _ _ _ = ?f _ _ _ _ _ |- _ => injection h; intros; clear h; subst
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end.
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Ltac go :=
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simpl in *;
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repeat match goal with
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| h: ?x = _ |- context[match ?x with _ => _ end] => rewrite h
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end;
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autoinjection;
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try (congruence);
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try omega;
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subst;
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eauto 4 with zarith datatypes;
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try (econstructor ; (solve[go])).
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Tactic Notation "go" := try (go; fail).
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Ltac go_with b :=
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simpl in *;
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repeat match goal with
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| h: ?x = _ |- context[match ?x with _ => _ end] => rewrite h
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end;
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autoinjection;
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try (congruence);
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try omega;
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subst;
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eauto 4 with zarith datatypes b;
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try (econstructor ; (solve[go])).
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Ltac inv H := inversion H; try subst; clear H.
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Tactic Notation "flatten" ident(H) :=
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repeat match goal with
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| H: context[match ?x with | left _ => _ | right _ => _ end] |- _ => destruct x
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| H: context[match ?x with | _ => _ end] |- _ => let E := fresh "Eq" in destruct x eqn:E
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end; autoinjection; try congruence.
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Tactic Notation "flatten" :=
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repeat match goal with
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| |- context[match ?x with | left _ => _ | right _ => _ end] => destruct x
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| |- context[match ?x with | _ => _ end] => let E := fresh "Eq" in destruct x eqn:E
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end; autoinjection; try congruence.
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(*Tactic Notation "induction" ident(x) := dependent induction x.*)
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Definition admit {T: Type} : T. Admitted.
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Tactic Notation "solve_by_inversion_step" tactic(t) :=
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match goal with
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| H : _ |- _ => solve [ inversion H; subst; t ]
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end
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|| fail "because the goal is not solvable by inversion.".
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Tactic Notation "solve" "by" "inversion" "1" :=
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solve_by_inversion_step idtac.
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Tactic Notation "solve" "by" "inversion" "2" :=
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solve_by_inversion_step (solve by inversion 1).
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Tactic Notation "solve" "by" "inversion" "3" :=
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solve_by_inversion_step (solve by inversion 2).
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Tactic Notation "solve" "by" "inversion" :=
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solve by inversion 1.
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