(** Type-safety proofs for Fsub.  Authors: Brian Aydemir and Arthur Chargu\'eraud, with help from Aaron Bohannon, Jeffrey Vaughan, and Dimitrios Vytiniotis.  In parentheses are given the label of the corresponding lemma in the appendix (informal proofs) of the POPLmark Challenge.  Table of contents: - #<a href="##subtyping">Properties of subtyping</a># - #<a href="##typing">Properties of typing</a># - #<a href="##preservation">Preservation</a># - #<a href="##progress">Progress</a># *)
Require Export Fsub.Fsub_LetSum_Lemmas.
(* ********************************************************************** *)
(** * #<a name="subtyping"></a># Properties of subtyping *)
(* ********************************************************************** *)
(** ** Reflexivity (1) *)
Proof with eauto.
intros E T Ok Wf.
induction Wf...
pick fresh Y and apply sub_all...
Qed.
(* ********************************************************************** *)
(** ** Weakening (2) *)

Lemma sub_weakening : forall E F G S T,
sub (G ++ E) S T ->
wf_env (G ++ F ++ E) ->
sub (G ++ F ++ E) S T.