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Ltac induction_with_subterm c H :=
let x := fresh "x" in
let y := fresh "y" in
(set(x := c) ; assert(y:x = c) by reflexivity ;
rewrite <- y in H ;
induction H ; subst).
Ltac induction_on_subterm c :=
let x := fresh "x" in
let y := fresh "y" in
(set(x := c) ; assert(y:x = c) by reflexivity ; clearbody x ; induction x ; inversion y ; try subst ;
clear y).
Ltac induction_with_subterms c c' H :=
let x := fresh "x" in
let y := fresh "y" in
let z := fresh "z" in
let w := fresh "w" in
(set(x := c) ; assert(y:x = c) by reflexivity ;
set(z := c') ; assert(w:z = c') by reflexivity ;
rewrite <- y in H ; rewrite <- w in H ;
induction H ; subst).
Ltac destruct_one_pair :=
match goal with
| [H : (ex _) |- _] => destruct H
| [H : (ex2 _) |- _] => destruct H
| [H : (sig _) |- _] => destruct H
| [H : (_ /\ _) |- _] => destruct H
end.
Ltac destruct_exists := repeat (destruct_one_pair) .
(* Destructs calls to f in hypothesis or conclusion, useful if f creates a subset object *)
Ltac destruct_call f :=
match goal with
| H : ?T |- _ =>
match T with
context [f ?x ?y ?z] => destruct (f x y z)
| context [f ?x ?y] => destruct (f x y)
| context [f ?x] => destruct (f x)
end
| |- ?T =>
match T with
context [f ?x ?y ?z] => let n := fresh "H" in set (n:=f x y z); destruct n
| context [f ?x ?y] => let n := fresh "H" in set (n:=f x y); destruct n
| context [f ?x] => let n := fresh "H" in set (n:=f x); destruct n
end
end.
Ltac myinjection :=
let tac H := inversion H ; subst ; clear H in
match goal with
| [ H : ?f ?a = ?f' ?a' |- _ ] => tac H
| [ H : ?f ?a ?b = ?f' ?a' ?b' |- _ ] => tac H
| [ H : ?f ?a ?b ?c = ?f' ?a' ?b' ?c' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d= ?f' ?a' ?b' ?c' ?d' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d ?e= ?f' ?a' ?b' ?c' ?d' ?e' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d ?e ?g= ?f' ?a' ?b' ?c' ?d' ?e' ?g' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d ?e ?g ?h= ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d ?e ?g ?h ?i = ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' ?i' |- _ ] => tac H
| [ H : ?f ?a ?b ?c ?d ?e ?g ?h ?i ?j = ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' ?i' ?j' |- _ ] => tac H
| _ => idtac
end.
Ltac destruct_nondep H := let H0 := fresh "H" in assert(H0 := H); destruct H0.
Ltac bang :=
match goal with
| |- ?x =>
match x with
| context [False_rect _ ?p] => elim p
end
end.
Ltac elim_eq_rect :=
match goal with
| [ |- ?t ] =>
match t with
context [ @eq_rect _ _ _ _ _ ?p ] => try case p ; simpl
end
end.
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