Ltac revert_all :=
repeat match goal with [ H : _ |- _ ] => revert H end.
Tactic Notation "revert" "all" := revert_all.
Ltac revert_except i :=
repeat match goal with [ H : _ |- _ ] => tryif unify H i then fail else revert H end.
Tactic Notation "revert" "all" "except" ident(i) := revert_except i.
Ltac clear_except i :=
repeat match goal with [ H : _ |- _ ] => tryif unify H i then fail else clear H end.
Tactic Notation "clear" "all" "except" ident(i) := clear_except i.
Ltac clear_all :=
repeat match goal with
[H : _ |- _] => clear H
end.
Ltac remember_arguments E :=
let tac x := (try (is_var x; fail 1); remember (x)) in
repeat (match type of E with
| ?t ?x _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ _ => tac x
| ?t ?x _ _ _ _ => tac x
| ?t ?x _ _ _ => tac x
| ?t ?x _ _ => tac x
| ?t ?x _ => tac x
| ?t ?x => tac x
end).
Ltac clear_dup :=
match goal with
| [ H : ?X |- _ ] =>
match goal with
| [ H' : ?Y |- _ ] =>
match H with
| H' => fail 2
| _ => unify X Y ; (clear H' || clear H)
end
end
end.
Ltac inv_eqs :=
repeat (match goal with
| [ H : @eq _ ?x ?x |- _ ] => fail
| [ H : @eq _ ?x ?y |- _ ] => progress (inversion H; subst; try clear_dup)
end).
Ltac clear_trivial_eqs :=
repeat (progress (match goal with
| [ H : @eq _ ?x ?x |- _ ] => clear H
end)).
Tactic Notation "general" "induction" hyp(H) :=
remember_arguments H; revert_except H;
induction H; intros; (try inv_eqs); (try clear_trivial_eqs).