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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
(* This needs step by step unfolding *)
Fixpoint T (n:nat) : Prop :=
match n with
| O => True
| S p => n = n -> T p
end.
Require Import Arith.
Goal T 3 -> T 1.
intro H.
apply H.
(* This needs unification on type *)
Goal forall n m : nat, S m = S n :>nat.
intros.
apply f_equal.
(* f_equal : forall (A B:Set) (f:A->B) (x y:A), x=y->(f x)=(f y) *)
(* and A cannot be deduced from the goal but only from the type of f, x or y *)
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