cleaning up proofs

proofs/spec/High/Zmodp2.v

@@ -149,94 +149,19 @@ Lemma mul_assoc : associative mul.
 Proof.
 move=> [x1 x2] [y1 y2] [z1 z2].
 solve_this.
-(* Zmodp2_unfold; ring_unfold.
-f_equal.
-f_equal.
-+ ring.
-+ ring. *)
-(*  ; apply val_inj => /=.
-+ rewrite Zminus_mod_idemp_r.
-  rewrite -(Zplus_mod (y1 * z1)).
-  rewrite Zmult_mod_idemp_r.
-  rewrite -(Zplus_mod (y1 * z2)).
-  rewrite Zmult_mod_idemp_r.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -Zplus_mod.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -(Zplus_mod (x1 * y1)).
-  rewrite Zmult_mod_idemp_l.
-  rewrite -(Zplus_mod (x1 * y2)).
-  rewrite Zmult_mod_idemp_l.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -Zplus_mod.
-  have ->: (x1 * (y1 * z1 + (p - y2 * z2)) + (p - x2 * (y1 * z2 + y2 * z1)) = 
-            x1 * (y1 * z1 + (- y2 * z2)) + (- x2 * (y1 * z2 + y2 * z1)) + (x1 + 1) * p)%Z by ring.
-  have ->: ((x1 * y1 + (p - x2 * y2)) * z1 + (p - (x1 * y2 + x2 * y1) * z2) = 
-            x1 * (y1 * z1 + (- y2 * z2)) + (- x2 * (y1 * z2 + y2 * z1)) + (z1 + 1) * p)%Z by ring.
-  by rewrite ?Z_mod_plus_full.
-+ rewrite Zminus_mod_idemp_r.
-  rewrite -(Zplus_mod (y1 * z2)).
-  rewrite Zmult_mod_idemp_r.
-  rewrite -(Zplus_mod (y1 * z1)).
-  rewrite Zmult_mod_idemp_r.
-  rewrite -Zplus_mod.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -(Zplus_mod (x1 * y1)).
-  rewrite Zmult_mod_idemp_l.
-  rewrite -(Zplus_mod (x1 * y2)).
-  rewrite Zmult_mod_idemp_l.
-  rewrite -Zplus_mod.
-  have ->: (x1 * (y1 * z2 + y2 * z1) + x2 * (y1 * z1 + (p - y2 * z2)) = 
-            x1 * (y1 * z2 + y2 * z1) + x2 * (y1 * z1 + ( - y2 * z2)) + (x2 * p))%Z by ring.
-  have ->: ((x1 * y1 + (p - x2 * y2)) * z2 + (x1 * y2 + x2 * y1) * z1 = 
-            x1 * (y1 * z2 + y2 * z1) + x2 * (y1 * z1 + ( - y2 * z2)) + (z2 * p))%Z by ring.
-  by rewrite ?Z_mod_plus_full. *)
+
 Qed.
 
 Lemma mul_left_id : left_id one mul.
 Proof.
 move=> [x1 x2].
 solve_this.
-(* Zmodp2_unfold; ring_unfold.
-rewrite Zmodp_ring.mul_left_id.
-rewrite Zmodp_ring.mul_left_id.
-have ->: Zmodp2 x1 x2 = pi (x1,x2) => //.
-f_equal ; f_equal ; Zmodp_ringify ; ring_simplify_this. *)
 Qed.
 
 Lemma mul_left_distr : left_distributive mul add.
 Proof.
 move=> [x1 x2] [y1 y2] [z1 z2].
 solve_this.
-(*  rewrite /mul /add /GRing.add /=. f_equal.
-f_equal.
-ring.
-ring.
- *)
-(* + apply val_inj => /=.
-  rewrite Zmult_mod_idemp_l.
-  rewrite Zmult_mod_idemp_l.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -Zplus_mod.
-  rewrite Zminus_mod_idemp_r.
-  rewrite Zminus_mod_idemp_r.
-  rewrite -(Zplus_mod (x1 * z1)).
-  rewrite -(Zplus_mod (y1 * z1)).
-  rewrite -Zplus_mod.
-  have ->: ((x1 + y1) * z1 + (p - (x2 + y2) * z2) = 
-          (x1 + y1) * z1 + - (x2 + y2) * z2 + 1 * p)%Z by ring.
-  have ->: (x1 * z1 + (p - x2 * z2) + (y1 * z1 + (p - y2 * z2)) = 
-          (x1 + y1) * z1 + - (x2 + y2) * z2 + 2 * p)%Z by ring.
-  by rewrite ?Z_mod_plus_full.
-+ apply val_inj => /=.
-  rewrite Zmult_mod_idemp_l.
-  rewrite Zmult_mod_idemp_l.
-  rewrite -Zplus_mod.
-  rewrite -(Zplus_mod (x1 * z2)).
-  rewrite -(Zplus_mod (y1 * z2)).
-  rewrite -Zplus_mod.
-  f_equal.
-  ring. *)
 Qed.
 
 Lemma one_neq_zero : one != zero.
@@ -283,16 +208,6 @@ Inductive Zinv_spec (x : type) : Type :=
 | Zinv_spec_zero : x = zero -> Zinv_spec x
 | Zinv_spec_unit : x <> zero -> forall y, (y * x)%R = one -> Zinv_spec x.
 
-(* Local Ltac ringify := repeat match goal with
-  | [ |- context[Zmodp.pi 2]] => rewrite pi_2
-  | [ |- context[Zmodp.mul ?a ?b]] => have ->: (Zmodp.mul a b) = a * b => //
-  | [ |- context[Zmodp.add ?a (Zmodp.opp ?b)]] => have ->: (Zmodp.add a (Zmodp.opp b)) = a - b => //
-  | [ |- context[Zmodp.opp ?a]] => have ->: Zmodp.opp a = -a => //
-  | [ |- context[Zmodp.add ?a ?b]] => have ->: (Zmodp.add a b) = a + b => //
-  | [ |- context[Zmodp.one] ] => have ->: Zmodp.one = 1 => //
-  | [ |- context[Zmodp.zero] ] => have ->: Zmodp.zero = 0 => //
-  end.
- *)
 Lemma Zinv x : Zinv_spec x.
 Proof.
 case_eq (eqb x zero) ; move/eqb_spec.

proofs/spec/High/Zmodp2_rules.v

@@ -11,27 +11,6 @@ Import GRing.Theory.
 Import Zmodp2.
 Import BinInt.
 
-(* Lemma expr3 : forall x:Zmodp2.type, x^+3 = x*x*x :> Zmodp2.type. *)
-(* Proof. move => x; rewrite ?exprSr expr0 GRing.mul1r //. Qed. *)
-
-(* Lemma expr3' : forall x:Zmodp.type, (x^+3 = x*x*x)%R. *)
-(* Proof. move => x; rewrite ?exprSr expr0 GRing.mul1r //. Qed. *)
-
-(* Ltac ring_simplify_this :=
-  repeat match goal with
-  | _ => rewrite GRing.exprS
-  | _ => rewrite GRing.expr0
-  | _ => rewrite GRing.mul1r
-  | _ => rewrite GRing.mulr1
-  | _ => rewrite GRing.mul0r
-  | _ => rewrite GRing.mulr0
-  | _ => rewrite GRing.add0r
-  | _ => rewrite GRing.oppr0
-  | _ => rewrite GRing.addr0
-  | _ => done
-end.
- *)
-
 Local Ltac unfolds := ring_unfold; Zmodp2_unfold.
 
 Ltac ringify := Zmodp_ringify ; Zmodp2_ringify.

proofs/spec/Libs/Bound_Decidable.v

-(* Set Warnings "-notation-overridden".
-
-Require Export Coq.ZArith.ZArith.
-(* Require Export Coq.Lists.List. *)
-(* Require Import Coq.Sorting.Sorting Orders. *)
-(* Require Import ssreflect. *)
-Require Import Tweetnacl.Libs.Decidable.
-(* Require Import Tweetnacl.Libs.Term_Decidable. *)
-
-Open Scope Z_scope.
-
-(* Local Instance term_dec : Decidable := 
-{
-  decide := term_decide;
-  denote := term_denote;
-  decide_impl := term_decide_impl
-}.
-
-*)
-Section Bound.
-
-(* Context {A:Type}.
- *)
-  Inductive bound :=
-    | LE_inf : Z -> Z -> bound
-    | LT_inf : Z -> Z -> bound
-    | LE_sup : Z -> Z -> bound
-    | LT_sup : Z -> Z -> bound.
-
-  Fixpoint expr_denote (env:environment) (m : bound) : Prop :=
-    match m with
-    | LE_inf z a => z <= a
-    | LT_inf z a => z < a
-    | LE_sup z a => a <= z
-    | LT_sup z a => a < z
-   end.
-
-  Inductive bound_formula :=
-    | Bound_sgl : bound -> bound_formula
-    | Bound_And : bound_formula -> bound_formula -> bound_formula
-    | Bound_Impl : bound_formula -> bound_formula.
-
-End Bound.
-
-
-Close Scope Z. *)
\ No newline at end of file

proofs/spec/Libs/Expr_Decidable.v

@@ -8,14 +8,6 @@ Require Import Tweetnacl.Libs.Decidable.
 Require Import Tweetnacl.Libs.Term_Decidable.
 
 Open Scope Z_scope.
-(*
-Instance term_dec : Decidable := 
-{
-  decide := term_eqb;
-  denote := term_denote;
-  decide_impl := term_eqb_impl
-}.
- *)
 
 Module TermOrder <: TotalLeBool.
     Definition t := term.

proofs/spec/Libs/Fun_Decidable.v

@@ -6,7 +6,7 @@ Open Scope Z_scope.
 
 Section fun_rec.
 
-Context {T:Type} (n:Z). (* (Hn : 0 <= n). *)
+Context {T:Type} (n:Z).
 
 Definition dec_proof_fun (n a  : Z) : nat := Z.to_nat (a - n).
 

proofs/spec/ListsOp/Forall_ZofList.v

@@ -4,8 +4,6 @@ From Tweetnacl Require Import Libs.Export.
 From Tweetnacl Require Export ListsOp.ZofList.
 Open Scope Z.
 
-(* Import ListNotations. *)
-
 Section Integer.
 
 Variable n:Z.
@@ -243,7 +241,6 @@ Proof.
         replace (n * S m) with (n * m + n).
         rewrite Zred_factor2 Z.pow_add_r ; try omega.
         apply Zmult_le_compat_l ; try omega.
-        
         assert(minilemma : forall a b, a < b -> 1 + a <= b).
           intros ; omega.
         apply minilemma.
@@ -310,8 +307,6 @@ Proof.
   reflexivity.
   simpl.
   orewrite Z.shiftl_mul_pow2.
-(*   replace ((ℤ.lst l) * 2 ^ n) with (2^n * (ℤ.lst l)). *)
-(*   2: rewrite Z.mul_comm ; reflexivity. *)
   rewrite -IHl.
   rewrite Zxor_add.
   f_equal.

proofs/spec/Low/Carry.v

@@ -59,8 +59,6 @@ Qed.
 End Integer.
 
 Close Scope Z.
-(* ADD LENGTH PROOF *)
-
 
 
 

proofs/spec/Low/Carry_n.v

@@ -95,11 +95,7 @@ Proof.
   clear Hi Hi' i Hi''' H17.
   rename H into Hi'.
   assert(HH : forall k, 0 ≤ getResidue 16 k ∧ getResidue 16 k < 2 ^ 16) by (clear ; intro; eapply getResidue_bounds ; omega).
-(*   change (2^62) with 4611686018427387904 in *.
-  change (2^63) with 9223372036854775808 in *.
-  change (2^16) with 65536 in *.
- *)
-   repeat match goal with
+  repeat match goal with
     | _ => rewrite Carry_n_step
     | _ => rewrite Carry_n_step_0
     | [H : _ \/ _ |- _ ] => destruct H ; try subst i'

proofs/spec/Low/Constant.v

@@ -12,8 +12,6 @@ Definition C_25519 := [65517;65535;65535;65535;65535;65535;65535;65535;65535;655
 
 End Low.
 
-(* Eval compute in ZofList 16 c_121665. *)
-
 Lemma C_121665_bounds : Forall (fun x0 : ℤ => 0 <= x0 < 2 ^ 16) Low.C_121665.
 Proof. unfold Low.C_121665;
 repeat match goal with

proofs/spec/Low/Get_abcdef.v

 Require Import Tweetnacl.Libs.Export.
 Require Export Tweetnacl.Gen.Get_abcdef.
 
-(*
-Definition get_b (t:(list Z * list Z * list Z * list Z * list Z * list Z)) : list Z := match t with
-  (a,b,c,d,e,f) => b
-end.
-Definition get_c (t:(list Z * list Z * list Z * list Z * list Z * list Z)) : list Z := match t with
-  (a,b,c,d,e,f) => c
-end.
-Definition get_d (t:(list Z * list Z * list Z * list Z * list Z * list Z)) : list Z := match t with
-  (a,b,c,d,e,f) => d
-end.
-Definition get_e (t:(list Z * list Z * list Z * list Z * list Z * list Z)) : list Z := match t with
-  (a,b,c,d,e,f) => e
-end.
-Definition get_f (t:(list Z * list Z * list Z * list Z * list Z * list Z)) : list Z := match t with
-  (a,b,c,d,e,f) => f
-end.
-*)
 Definition get_m (c:(list Z * list Z)) : list Z := match c with
   (m,t) => m
 end.

proofs/spec/Low/Reduce_by_P_compose_2b.v

@@ -124,11 +124,6 @@ Local Ltac solve_this_assert :=
   eapply Forall_take_n_m ; [| eauto];
   Grind_add_Z ; change_Z_to_nat ; omega.
 
-(*   rewrite sub_fn_rev_s_n; try omega;
-  rewrite sub_step_2_Z_inv_lss; Grind_add_Z; try assumption;
-  rewrite ?sub_fn_rev_s_sub_step_2_Zlength ; try omega;
-  apply bound_a_subst_step_2_lss ; auto ; omega.
- *)
 Local Ltac gen_goals P j n := match n with
   | 0 => idtac
   | n =>
@@ -163,14 +158,6 @@ assert(H2: ℤ16.lst sub_fn_rev_s 1 sub_step_2 2 m = ℤ16.lst m).
   rewrite sub_fn_rev_s_n ; try apply sub_step_2_Z_inv_lss; [omega | | omega].
   assert(Haspe: 0 < 2 - 1 /\ 2 - 1 < 16) by omega.
   apply Hbound in Haspe; omega.
-(* assert ((fun x => (ℤ16.lst sub_fn_rev_s 1 sub_step_2 x m = ℤ16.lst m)) 3).
-  rewrite sub_fn_rev_s_n; try omega;
-  rewrite sub_step_2_Z_inv_lss; Grind_add_Z; try assumption;
-  rewrite ?sub_fn_rev_s_sub_step_2_Zlength ; try omega;
-  apply bound_a_subst_step_2_lss ; auto ; try omega;
-  eapply Forall_take_n_m ; [| eauto];
-  Grind_add_Z ; change_Z_to_nat ; omega.
- *)
 gen_goals (fun x => (ℤ16.lst sub_fn_rev_s 1 sub_step_2 x m = ℤ16.lst m)) 16 13.
 assert_gen_hyp_ Hadec a 15 14 ; try omega.
 repeat match goal with

proofs/spec/Low/ScalarMult_rev.v

@@ -85,7 +85,6 @@ Local Ltac solve_dependencies_bound :=
 repeat match goal with
   | _ => assumption
   | _ => reflexivity
-(*   | _ => solve_dependencies_length *)
   | _ => apply M_bound_Zlength
   | _ => apply Sq_bound_Zlength
   | _ => apply A_bound_Zlength_le

proofs/spec/Mid/Mod.v

-From Tweetnacl Require Import Libs.Export.
-Require Import ssreflect.
+Require Import ZArith.
 
 Local Open Scope Z.
 Definition modP x := Z.modulo x (Z.pow 2 255 - 19).

proofs/spec/Mid/Prep_n.v

@@ -38,11 +38,6 @@ Z.ones 8;Z.ones 8;Z.ones 8;Z.ones 8;Z.ones 8;Z.ones 8;Z.ones 8;127]). *)
 Definition Zclamp (n : Z) : Z :=
   (Z.lor (Z.land n (Z.land (Z.ones 255) (-8))) (Z.shiftl 64 (31 * 8))).
 
-(*
-Lemma Zclamp_eq : forall n,
-  Zclamp' n = Zclamp n.
-Proof. done. Qed.
-*)
 Lemma Zclamp_min n : 0 <= Zclamp n.
 Proof.
 rewrite /Zclamp.

proofs/spec/Mid/Reduce.v

@@ -3,8 +3,6 @@ Require Import ssreflect.
 
 Open Scope Z.
 
-(*Notation "A :𝓖𝓕" := (A mod (2^255 - 19)) (at level 80, right associativity).*)
-
 Lemma t2256is38 : (2^256 :𝓖𝓕 ) = (38 :𝓖𝓕).
 Proof.
   compute ; reflexivity.

proofs/vst/proofs/verif_A.v

@@ -98,14 +98,7 @@ all: clean_context_from_VST.
 all: rewrite /tkdp -?map_firstn -?map_skipn -?map_app in HHaux3.
 all: rewrite /tkdp -?map_firstn -?map_skipn -?map_app in HHaux4.
 all: inv HHaux1 ; inv HHaux2 ; inv HHaux3 ; inv HHaux4.
-(* all: rewrite ?(Znth_map 0) ?take_drop_Zlength ; try omega. *)
 all: rewrite add64_repr /nat_of_Z.
-(* all: rewrite ?app_Znth2. *)
-(* all: try replace (Zlength (firstn (Z.to_nat i) (A _ _))) with i. *)
-(* all: rewrite ?Znth_skipn. *)
-(* all: rewrite ?Zlength_firstn ?HA. *)
-(* all: rewrite ?Z.max_r ?Z.min_l ; try omega. *)
-(* all: replace (i - i + i) with i by omega. *)
 all: rewrite ?Znth_nth; try omega.
 all: rewrite <- ZsubList_nth_Zlength ; try omega.
 all: rewrite /tkdp ?simple_S_i ; try omega.

proofs/vst/proofs/verif_M_compute.v

@@ -32,22 +32,6 @@ Local Instance list_term_dec : Decidable := Build_Decidable
 
 Local Ltac solve_this_thing_please_autorewrite i j:= 
     subst i;
-(*    let H' := fresh in
-    gen_i H' j ; simpl;
-    repeat rewrite outer_M_i_j_eq by abstract omega;
-    repeat rewrite inner_M_i_j_eq by abstract omega;
-    repeat rewrite Znth_nth by abstract omega;
-    repeat rewrite upd_Znth_upd_nth by omega;
-    Grind_add_Z;
-    compute;
-    repeat rewrite Z.add_0_r;
-    repeat rewrite Z.add_0_l;
-    repeat rewrite Z.add_assoc;
-    reflexivity.
-
-  Opaque Z.add.
-  Opaque Z.mul.*)
-
     let H' := fresh in
     gen_i H' j ; simpl;
     repeat orewrite inner_M_i_j_eq;
@@ -101,26 +85,6 @@ Proof.
     repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]).
     solve_this_thing_please_autorewrite i j.
 Qed.
-(*
-  intros i j a b Ha Hb Hi Hj Hii.
-  rewrite Zlength_correct in Ha.
-  rewrite Zlength_correct in Hb.
-  assert(Ha' : (length a = 16)%nat) by go.
-  assert(Hb' : (length b = 16)%nat) by go.
-  repeat (destruct a ; tryfalse).
-  repeat (destruct b ; tryfalse).
-  rewrite <- Zlength_correct in *.
-  rewrite (outer_M_fix_equation i).
-  flatten.
-    apply Z.leb_le in Eq ; omega.
-    clear Eq.
-  assert(H: i = 0 \/ i = 1 \/ i = 2 \/ i = 3) by omega.
-    destruct H ; try (subst i ; omega).
-  Opaque outer_M_fix.
-    repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]). (* i = 1 -> 14 *)
-    solve_this_thing_please_autorewrite i j.
-Qed.
-*)
 
 Lemma outer_M_fix_i_1'' : forall i j contents_a contents_b,
 Zlength contents_a = 16 ->
@@ -161,26 +125,6 @@ Proof.
     repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]).
     solve_this_thing_please_autorewrite i j.
 Qed.
-(* Admitted. *)
-(*
-  intros i j a b Ha Hb Hi Hj Hii.
-  rewrite Zlength_correct in Ha.
-  rewrite Zlength_correct in Hb.
-  assert(Ha' : (length a = 16)%nat) by go.
-  assert(Hb' : (length b = 16)%nat) by go.
-  repeat (destruct a ; tryfalse).
-  repeat (destruct b ; tryfalse).
-  rewrite <- Zlength_correct in *.
-  rewrite (outer_M_fix_equation i).
-  flatten.
-    apply Z.leb_le in Eq ; omega.
-    clear Eq.
-  assert(H: i = 4 \/ i = 5 \/ i = 6 \/ i = 7) by omega.
-  Opaque outer_M_fix.
-    repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]). (* i = 1 -> 14 *)
-    solve_this_thing_please_autorewrite i j. (* i = 15 *)
-Qed.
-*)
 
 Lemma outer_M_fix_i_1''' : forall i j contents_a contents_b,
 Zlength contents_a = 16 ->
@@ -221,26 +165,6 @@ Proof.
     repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]).
     solve_this_thing_please_autorewrite i j.
 Qed.
-(* Admitted. *)
-(*
-  intros i j a b Ha Hb Hi Hj Hii.
-  rewrite Zlength_correct in Ha.
-  rewrite Zlength_correct in Hb.
-  assert(Ha' : (length a = 16)%nat) by go.
-  assert(Hb' : (length b = 16)%nat) by go.
-  repeat (destruct a ; tryfalse).
-  repeat (destruct b ; tryfalse).
-  rewrite <- Zlength_correct in *.
-  rewrite (outer_M_fix_equation i).
-  flatten.
-    apply Z.leb_le in Eq ; omega.
-    clear Eq.
-  assert(H: i = 8 \/ i = 9 \/ i = 10 \/ i = 11 \/ i = 12) by omega.
-  Opaque outer_M_fix.
-    repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]). (* i = 1 -> 14 *)
-    solve_this_thing_please_autorewrite i j. (* i = 15 *)
-Qed.
-*)
 
 Lemma outer_M_fix_i_1'''' : forall i j contents_a contents_b,
 Zlength contents_a = 16 ->
@@ -282,26 +206,6 @@ Proof.
     repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]).
     solve_this_thing_please_autorewrite i j.
 Qed.
-(* Admitted. *)
-(* 
-  intros i j a b Ha Hb Hi Hj Hii.
-  rewrite Zlength_correct in Ha.
-  rewrite Zlength_correct in Hb.
-  assert(Ha' : (length a = 16)%nat) by go.
-  assert(Hb' : (length b = 16)%nat) by go.
-  repeat (destruct a ; tryfalse).
-  repeat (destruct b ; tryfalse).
-  rewrite <- Zlength_correct in *.
-  rewrite (outer_M_fix_equation i).
-  flatten.
-    apply Z.leb_le in Eq ; omega.
-    clear Eq.
-  assert(H: i = 12 \/ i = 13 \/ i = 14 \/ i = 15) by omega.
-  Opaque outer_M_fix.
-    repeat (destruct H ; [solve_this_thing_please_autorewrite i j|]). (* i = 1 -> 14 *)
-    solve_this_thing_please_autorewrite i j. (* i = 15 *)
-Qed.
-*)
 
 Lemma outer_M_fix_i_1 : forall i j contents_a contents_b,
 Zlength contents_a = 16 ->

proofs/vst/proofs/verif_crypto_scalarmult_lemmas.v

@@ -253,7 +253,7 @@ Lemma data_at_sh_if : forall T SH i a b p ,
   = data_at SH T (if 254 =? i then a else b) p.
 Proof. intros ; flatten. Qed.
 
-Local Ltac solve_lengths H48 H4 H5 H6 H7 := repeat match goal with 
+(* Local Ltac solve_lengths H48 H4 H5 H6 H7 := repeat match goal with 
     | _ => omega
     | _ => rewrite H48
     | _ => rewrite H4
@@ -270,8 +270,8 @@ Local Ltac solve_lengths2 := repeat match goal with
     | _ => rewrite undef16_Zlength
     | _ => rewrite Zlength_map
   end.
-
-Lemma replace_list_app_app_app_app : forall i xx aa bb cc dd va vb vc vd,
+ *)
+(* Lemma replace_list_app_app_app_app : forall i xx aa bb cc dd va vb vc vd,
   0 <= i < 16 ->
   Zlength aa = 16 ->
   Zlength bb = 16 ->
@@ -412,14 +412,5 @@ Proof.
   rewrite ?simple_S_i ; try omega;
   rewrite ?Hvd ?Hvb -upd_Znth_app_step_Zlength ; solve_lengths2.
 Qed.
-
-(* Definition sc_mult n p :=
-  let p' := Unpack25519 p in
-  let n' := clamp n in
-  let m  := montgomery_fn 255 254 n' gf1 p' gf0 gf1 gf0 gf0 p' in
-  let c  := get_c m in 
-  let c' := Inv25519 c in 
-  let a  := get_a m in
-  Pack25519 (M a c').
  *)
 Close Scope Z.

proofs/vst/proofs/verif_inv25519.v

@@ -213,7 +213,6 @@ all: remember (pow_fn_rev 254 254 i i) as p. (* the expension is always anoying.
 
 (* Goal 1 *)
 1,2: freeze_local L.
-(* rewrite {1}/Sfor. (* because forward_for_simple_bound does not work otherwise *) *)
 1: forward_for_simple_bound 16 (copy_Inv L sho shi Tsh v_o v_o v_c (mVI64 i) i p 0) ; subst L.
 1: thaw_local.
 4: forward_for_simple_bound 16 (copy_Inv L sho shi Tsh v_o v_i v_c o i p 1) ; subst L.