diff options
Diffstat (limited to 'backend/Asmgenproof0.v')
| -rw-r--r-- | backend/Asmgenproof0.v | 44 |
1 files changed, 22 insertions, 22 deletions
diff --git a/backend/Asmgenproof0.v b/backend/Asmgenproof0.v index 3638c465..85cee14f 100644 --- a/backend/Asmgenproof0.v +++ b/backend/Asmgenproof0.v @@ -31,7 +31,7 @@ Require Import Conventions. (** * Processor registers and register states *) -Hint Extern 2 (_ <> _) => congruence: asmgen. +Global Hint Extern 2 (_ <> _) => congruence: asmgen. Lemma ireg_of_eq: forall r r', ireg_of r = OK r' -> preg_of r = IR r'. @@ -56,7 +56,7 @@ Lemma preg_of_data: Proof. intros. destruct r; reflexivity. Qed. -Hint Resolve preg_of_data: asmgen. +Global Hint Resolve preg_of_data: asmgen. Lemma data_diff: forall r r', @@ -64,7 +64,7 @@ Lemma data_diff: Proof. congruence. Qed. -Hint Resolve data_diff: asmgen. +Global Hint Resolve data_diff: asmgen. Lemma preg_of_not_SP: forall r, preg_of r <> SP. @@ -78,7 +78,7 @@ Proof. intros. apply data_diff; auto with asmgen. Qed. -Hint Resolve preg_of_not_SP preg_of_not_PC: asmgen. +Global Hint Resolve preg_of_not_SP preg_of_not_PC: asmgen. Lemma nextinstr_pc: forall rs, (nextinstr rs)#PC = Val.offset_ptr rs#PC Ptrofs.one. @@ -473,7 +473,7 @@ Inductive code_tail: Z -> code -> code -> Prop := Lemma code_tail_pos: forall pos c1 c2, code_tail pos c1 c2 -> pos >= 0. Proof. - induction 1. omega. omega. + induction 1. lia. lia. Qed. Lemma find_instr_tail: @@ -484,8 +484,8 @@ Proof. induction c1; simpl; intros. inv H. destruct (zeq pos 0). subst pos. - inv H. auto. generalize (code_tail_pos _ _ _ H4). intro. omegaContradiction. - inv H. congruence. replace (pos0 + 1 - 1) with pos0 by omega. + inv H. auto. generalize (code_tail_pos _ _ _ H4). intro. extlia. + inv H. congruence. replace (pos0 + 1 - 1) with pos0 by lia. eauto. Qed. @@ -494,8 +494,8 @@ Remark code_tail_bounds_1: code_tail ofs fn c -> 0 <= ofs <= list_length_z fn. Proof. induction 1; intros; simpl. - generalize (list_length_z_pos c). omega. - rewrite list_length_z_cons. omega. + generalize (list_length_z_pos c). lia. + rewrite list_length_z_cons. lia. Qed. Remark code_tail_bounds_2: @@ -505,8 +505,8 @@ Proof. assert (forall ofs fn c, code_tail ofs fn c -> forall i c', c = i :: c' -> 0 <= ofs < list_length_z fn). induction 1; intros; simpl. - rewrite H. rewrite list_length_z_cons. generalize (list_length_z_pos c'). omega. - rewrite list_length_z_cons. generalize (IHcode_tail _ _ H0). omega. + rewrite H. rewrite list_length_z_cons. generalize (list_length_z_pos c'). lia. + rewrite list_length_z_cons. generalize (IHcode_tail _ _ H0). lia. eauto. Qed. @@ -531,7 +531,7 @@ Lemma code_tail_next_int: Proof. intros. rewrite Ptrofs.add_unsigned, Ptrofs.unsigned_one. rewrite Ptrofs.unsigned_repr. apply code_tail_next with i; auto. - generalize (code_tail_bounds_2 _ _ _ _ H0). omega. + generalize (code_tail_bounds_2 _ _ _ _ H0). lia. Qed. (** [transl_code_at_pc pc fb f c ep tf tc] holds if the code pointer [pc] points @@ -654,7 +654,7 @@ Opaque transl_instr. exists (Ptrofs.repr ofs). red; intros. rewrite Ptrofs.unsigned_repr. congruence. exploit code_tail_bounds_1; eauto. - apply transf_function_len in TF. omega. + apply transf_function_len in TF. lia. + exists Ptrofs.zero; red; intros. congruence. Qed. @@ -663,7 +663,7 @@ End RETADDR_EXISTS. Remark code_tail_no_bigger: forall pos c1 c2, code_tail pos c1 c2 -> (length c2 <= length c1)%nat. Proof. - induction 1; simpl; omega. + induction 1; simpl; lia. Qed. Remark code_tail_unique: @@ -671,8 +671,8 @@ Remark code_tail_unique: code_tail pos fn c -> code_tail pos' fn c -> pos = pos'. Proof. induction fn; intros until pos'; intros ITA CT; inv ITA; inv CT; auto. - generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega. - generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; omega. + generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; lia. + generalize (code_tail_no_bigger _ _ _ H3); simpl; intro; lia. f_equal. eauto. Qed. @@ -713,13 +713,13 @@ Proof. case (is_label lbl a). intro EQ; injection EQ; intro; subst c'. exists (pos + 1). split. auto. split. - replace (pos + 1 - pos) with (0 + 1) by omega. constructor. constructor. - rewrite list_length_z_cons. generalize (list_length_z_pos c). omega. + replace (pos + 1 - pos) with (0 + 1) by lia. constructor. constructor. + rewrite list_length_z_cons. generalize (list_length_z_pos c). lia. intros. generalize (IHc (pos + 1) c' H). intros [pos' [A [B C]]]. exists pos'. split. auto. split. - replace (pos' - pos) with ((pos' - (pos + 1)) + 1) by omega. + replace (pos' - pos) with ((pos' - (pos + 1)) + 1) by lia. constructor. auto. - rewrite list_length_z_cons. omega. + rewrite list_length_z_cons. lia. Qed. (** Helper lemmas to reason about @@ -746,7 +746,7 @@ Qed. Definition nolabel (i: instruction) := match i with Plabel _ => False | _ => True end. -Hint Extern 1 (nolabel _) => exact I : labels. +Global Hint Extern 1 (nolabel _) => exact I : labels. Lemma tail_nolabel_cons: forall i c k, @@ -757,7 +757,7 @@ Proof. intros. simpl. rewrite <- H1. destruct i; reflexivity || contradiction. Qed. -Hint Resolve tail_nolabel_refl: labels. +Global Hint Resolve tail_nolabel_refl: labels. Ltac TailNoLabel := eauto with labels; |