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Lemma test1 :
forall (v : nat) (f g : nat -> nat),
f v = g v.
intros. f_equal.
(*
Goal in v8.5: f v = g v
Goal in v8.4: v = v -> f v = g v
Expected: f = g
*)
Admitted.
Lemma test2 :
forall (v u : nat) (f g : nat -> nat),
f v = g u.
intros. f_equal.
(*
In both v8.4 And v8.5
Goal 1: v = u -> f v = g u
Goal 2: v = u
Expected Goal 1: f = g
Expected Goal 2: v = u
*)
Admitted.
Lemma test3 :
forall (v : nat) (u : list nat) (f : nat -> nat) (g : list nat -> nat),
f v = g u.
intros. f_equal.
(*
In both v8.4 And v8.5, the goal is unchanged.
*)
Admitted.
Require Import List.
Lemma foo n (l k : list nat) : k ++ skipn n l = skipn n l.
Proof. f_equal.
(*
8.4: leaves the goal unchanged, i.e. k ++ skipn n l = skipn n l
8.5: 2 goals, skipn n l = l -> k ++ skipn n l = skipn n l
and skipn n l = l
*)
Require Import List.
Fixpoint replicate {A} (n : nat) (x : A) : list A :=
match n with 0 => nil | S n => x :: replicate n x end.
Lemma bar {A} n m (x : A) :
skipn n (replicate m x) = replicate (m - n) x ->
skipn n (replicate m x) = replicate (m - n) x.
Proof. intros. f_equal.
(* 8.5: one goal, n = m - n *)
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