From Stdlib Require Import Strings.String.
From Stdlib Require Import String Ascii.
From Stdlib Require Arith.
From stdpp Require Import base.
From stdpp Require Import fin_maps.
From stdpp Require Import gmap.
From stdpp Require Import base gmultiset.
From Stdlib Require Classical.
From Stdlib Require Import ZArith.
From stdpp.bitvector Require Import definitions tactics.
From Stdlib Require Import Sorting.Sorted.
From Stdlib Require Import Reals.Rbasic_fun.
From Stdlib Require Import Reals.Abstract.ConstructiveAbs.
From Stdlib Require Import Reals.Rdefinitions.
From stdpp Require Import list_relations.
From stdpp Require Import list_numbers.
From stdpp Require Import functions.
From Stdlib Require Import ClassicalEpsilon.
From stdpp Require Import base decidable.
From Stdlib Require Import ZArith.Zeuclid.
From Stdlib Require Import ZArith.Znumtheory.
From stdpp Require Import propset.
From Stdlib Require Import Reals.
Require Import Why3.Base.
Require Import Why3.Qed.Qed.
Require Import Why3.Memory.Memory.
Require Import Why3.Cint.Cint.
Require Import x509_parser.Compound.Compound.
Require Import Why3.Cbits.Cbits.
Open Scope Z_scope.
Lemma goal2 (a_2 : addr) (a : addr) (a_1 : addr) (i_6 : Z) (i_8 : Z) (t_2 : addr -> Z) (t_1 : addr -> Z) (i_1 : Z) (i_2 : Z) (i_5 : Z) (i_3 : Z) (t : Z -> Z) (i : Z) (i_7 : Z) (i_9 : Z) (i_4 : Z) : let x : Z := base a_2 in let x_1 : Z := base a in let x_2 : Z := base a_1 in let x_3 : Z := i_6 + i_8 in let x_4 : Z := t_2 a in let m : addr -> Z := fun_updt t_1 a (to_uint16 x_3) in let a_3 : addr := shift a_1 12%Z in let x_5 : Z := m a_3 in let a_4 : addr := shift a_2 i_6 in let a_5 : addr := shift a_2 (i_1 + i_6) in let x_7 : Z := 2147483647%Z + i_2 in let x_8 : Z := 2147483648%Z + i_8 in ¬ i_5 = 0%Z -> ¬ Mk_addr 0%Z 0%Z = a_2 -> ¬ x = x_1 -> ¬ x = x_2 -> i_3 < 0%Z -> 0%Z ≤ i_5 -> i_6 ≤ i_5 -> i_8 ≤ i_5 -> 0%Z ≤ i_8 -> x_3 ≤ i_5 -> region x_1 ≤ 0%Z -> region x_2 ≤ 0%Z -> region x ≤ 0%Z -> 2%Z ≤ i_6 -> - 2147483648%Z ≤ x_3 -> x_3 ≤ 2147483647%Z -> linked t -> is_uint16 i -> is_uint16 i_1 -> is_uint16 i_2 -> is_uint16 i_5 -> is_uint16 i_6 -> is_uint16 i_7 -> is_uint16 i_8 -> is_uint16 i_9 -> is_sint32 i_3 -> is_sint32 i_4 -> is_uint16 x_4 -> valid_rw t a 1%Z -> valid_rw t a_1 15%Z -> separated a 1%Z a_1 15%Z -> is_sint32 x_5 -> (if decide (i_4 = 0%Z) then ¬ i = 0%Z ∧ ¬ i_8 = 0%Z ∧ ¬ a_4 = Mk_addr 0%Z 0%Z ∧ ¬ a_5 = Mk_addr 0%Z 0%Z ∧ to_uint16 (i - i_2) = 0%Z ∧ to_uint16 (i_8 - i_1) = i ∧ fun_updt m a_3 x_5 = t_2 ∧ i_2 ≤ i ∧ i_1 ≤ i_8 ∧ 2%Z ≤ i_2 ∧ i ≤ x_7 ∧ i_1 ≤ x_8 ∧ i_2 ≤ 2147483648%Z + i ∧ i_8 ≤ 2147483647%Z + i_1 ∧ valid_rd t a_3 1%Z ∧ valid_rw t a_3 1%Z ∧ (0%Z < i -> valid_rd t a_5 i) else ¬ i_8 = 0%Z ∧ i_8 = i ∧ ¬ a_4 = Mk_addr 0%Z 0%Z ∧ to_uint16 (i_8 - i_2) = 0%Z ∧ fun_updt m a_3 (lor 1%Z x_5) = t_2 ∧ i_2 ≤ i_8 ∧ 2%Z ≤ i_2 ∧ i_2 ≤ x_8 ∧ i_8 ≤ x_7 ∧ valid_rd t a_3 1%Z ∧ valid_rw t a_3 1%Z) -> (i_8 = 0%Z -> i_4 < 0%Z) -> (i_4 = 0%Z -> i_9 ≤ i_8) -> (a_4 = Mk_addr 0%Z 0%Z -> i_4 < 0%Z) -> (i_4 = 0%Z -> i_7 + i_9 ≤ i_8) -> (i_4 = 0%Z -> i_7 ≤ i_8 ∧ 2%Z ≤ i_7) -> (0%Z < i_5 -> valid_rd t (shift a_2 0%Z) i_5) -> (¬ a_4 = Mk_addr 0%Z 0%Z -> 0%Z < i_8 -> valid_rd t a_4 i_8) -> i_4 = 0%Z ∨ i_4 < 0%Z -> 0%Z < x_4 ∧ x_4 ≤ i_5.
Admitted.
