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.
Open Scope Z_scope.
Lemma goal0 (a_2 : addr) (a : addr) (i_8 : Z) (i_12 : Z) (i_10 : Z) (a_1 : addr) (i_9 : Z) (i_7 : Z) (t : Z -> Z) (i : Z) (i_1 : Z) (i_11 : Z) (i_13 : Z) (i_14 : Z) (i_15 : Z) (i_2 : Z) (i_3 : Z) (i_4 : Z) (i_5 : Z) (i_6 : Z) (i_16 : Z) : let x : Z := base a_2 in let x_1 : Z := base a in let x_2 : Z := i_8 + i_12 in let x_3 : Z := 2147483647%Z + i_10 in let a_3 : addr := shift a_1 (i_9 + i_10) in let a_4 : addr := shift a_1 i_9 in ¬ i_7 = 0%Z -> ¬ Mk_addr 0%Z 0%Z = a_2 -> ¬ x = x_1 -> 0%Z ≤ i_7 -> region x_1 ≤ 0%Z -> region x ≤ 0%Z -> linked t -> is_uint16 i -> is_uint16 i_1 -> is_uint16 i_7 -> is_uint16 i_8 -> is_uint16 i_9 -> is_uint16 i_10 -> is_uint16 i_11 -> is_uint16 i_12 -> is_uint16 i_13 -> is_uint16 i_14 -> is_uint16 i_15 -> is_sint32 i_2 -> is_sint32 i_3 -> is_sint32 i_4 -> is_sint32 i_5 -> is_sint32 i_6 -> is_sint32 i_16 -> valid_rw t a 15%Z -> (if decide (i_16 = 0%Z) then i_4 = - 6215%Z else (if decide (i_2 = 0%Z) then - 2147483648%Z ≤ x_2 ∧ x_2 ≤ 2147483647%Z ∧ (if decide (x_2 = i_7) then valid_rd t (shift a_1 0%Z) i_1 ∧ (if decide (i_1 = 0%Z) then i_4 = 0%Z else 0%Z ≤ i_1 ∧ (if decide (i_3 = 0%Z) then to_uint16 (i_1 - i_9) = i ∧ 0%Z ≤ i_13 ∧ i_1 ≤ 2147483647%Z + i_9 ∧ i_9 ≤ 2147483648%Z + i_1 ∧ (if decide (i_5 = 0%Z) then to_uint16 (i_13 - i_10) = i_14 ∧ i ≤ x_3 ∧ i_10 ≤ 2147483648%Z + i ∧ i_10 ≤ 2147483648%Z + i_13 ∧ i_13 ≤ x_3 ∧ (if decide (i_6 = 0%Z) then i_4 = - 6279%Z ∧ ¬ i_15 = 0%Z ∧ to_uint16 (i_14 - i_11) = i_15 ∧ i_11 ≤ 2147483648%Z + i_14 ∧ i_14 ≤ 2147483647%Z + i_11 else i_6 = i_4) ∧ (i_14 = 0%Z -> i_6 < 0%Z) ∧ (i_6 = 0%Z -> i_11 ≤ i_14 ∧ 3%Z ≤ i_11) ∧ (a_3 = Mk_addr 0%Z 0%Z -> i_6 < 0%Z) ∧ (¬ a_3 = Mk_addr 0%Z 0%Z -> 0%Z < i_14 -> valid_rd t a_3 i_14) ∧ (i_6 = 0%Z ∨ i_6 < 0%Z) else i_5 = i_4) ∧ (i_13 = 0%Z -> i_5 < 0%Z) ∧ (a_4 = Mk_addr 0%Z 0%Z -> i_5 < 0%Z) ∧ (i_5 = 0%Z -> i_10 ≤ i_13 ∧ 3%Z ≤ i_10) ∧ (¬ a_4 = Mk_addr 0%Z 0%Z -> 0%Z < i_13 -> valid_rd t a_4 i_13) ∧ (i_5 = 0%Z ∨ i_5 < 0%Z) else i_4 = i_3) ∧ (Mk_addr 0%Z 0%Z = a_1 -> i_3 < 0%Z) ∧ (i_3 = 0%Z -> i_13 ≤ i_1) ∧ (i_3 = 0%Z -> i_9 + i_13 ≤ i_1) ∧ (i_3 = 0%Z -> i_9 ≤ i_1 ∧ 2%Z ≤ i_9) ∧ (i_3 = 0%Z ∨ i_3 < 0%Z)) else i_4 = - 6232%Z) else i_4 = i_2) ∧ (i_2 = 0%Z -> i_12 ≤ i_7) ∧ (i_2 = 0%Z -> x_2 ≤ i_7) ∧ (i_2 = 0%Z -> i_8 ≤ i_7 ∧ 2%Z ≤ i_8) ∧ (i_2 = 0%Z ∨ i_2 < 0%Z)) -> (0%Z < i_7 -> valid_rd t (shift a_2 0%Z) i_7) -> i_4 ≤ 0%Z.
Admitted.
