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Goal forall a b c : nat, a = b -> b = c -> forall d, a+d=c+d.
intros.
(* "compatibility" mode: specializing a global name
means a kind of generalize *)
specialize eq_trans. intros _.
specialize eq_trans with (1:=H)(2:=H0). intros _.
specialize eq_trans with (x:=a)(y:=b)(z:=c). intros _.
specialize eq_trans with (1:=H)(z:=c). intros _.
specialize eq_trans with nat a b c. intros _.
specialize (@eq_trans nat). intros _.
specialize (@eq_trans _ a b c). intros _.
specialize (eq_trans (x:=a)). intros _.
specialize (eq_trans (x:=a)(y:=b)). intros _.
specialize (eq_trans H H0). intros _.
specialize (eq_trans H0 (z:=b)). intros _.
(* local "in place" specialization *)
assert (Eq:=eq_trans).
specialize Eq.
specialize Eq with (1:=H)(2:=H0). Undo.
specialize Eq with (x:=a)(y:=b)(z:=c). Undo.
specialize Eq with (1:=H)(z:=c). Undo.
specialize Eq with nat a b c. Undo.
specialize (Eq nat). Undo.
specialize (Eq _ a b c). Undo.
(* no implicit argument for Eq, hence no (Eq (x:=a)) *)
specialize (Eq _ _ _ _ H H0). Undo.
specialize (Eq _ _ _ b H0). Undo.
(*
(** strange behavior to inspect more precisely *)
(* 1) proof aspect : let H:= ... in (fun H => ..) H
presque ok... *)
(* 2) echoue moins lorsque zero premise de mangé *)
specialize eq_trans with (1:=Eq). (* mal typé !! *)
(* 3) *)
specialize eq_trans with _ a b c. intros _.
(* Anomaly: Evar ?88 was not declared. Please report. *)
*)
Abort.
(* Test use of pose proof and assert as a specialize *)
Goal True -> (True -> 0=0) -> False -> 0=0.
intros H0 H H1.
pose proof (H I) as H.
(* Check that the hypothesis is in 2nd position by removing the top one *)
match goal with H:_ |- _ => clear H end.
match goal with H:_ |- _ => exact H end.
Qed.
Goal True -> (True -> 0=0) -> False -> 0=0.
intros H0 H H1.
assert (H:=H I).
(* Check that the hypothesis is in 2nd position by removing the top one *)
match goal with H:_ |- _ => clear H end.
match goal with H:_ |- _ => exact H end.
Qed.
(* Test specialize as *)
Goal (forall x, x=0) -> 1=0.
intros.
specialize (H 1) as ->.
reflexivity.
Qed.
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