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 x509_parser.Globals.Globals.
Open Scope Z_scope.
Theorem goal1 (a_5 : addr) (i_7 : Z) (i_5 : Z) (i_8 : Z) (t_3 : addr -> Z) (a_2 : addr) (i : Z) (a_3 : addr) (i_3 : Z) (i_10 : Z) (i_6 : Z) (i_11 : Z) (i_4 : Z) (a_1 : addr) (a_4 : addr) (t_4 : addr -> addr) (t_1 : Z -> Z) (i_1 : Z) (i_9 : Z) (i_2 : Z) (t_2 : addr -> Z) (t : Z -> Z) : let a_6 : addr := shift a_5 i_7 in let a_7 : addr := shift___anonstruct__ext_oid_14 (Mk_addr (- 4284%Z) 0%Z) i_5 in let x : Z := i_7 + i_8 in let x_1 : Z := fun_updt t_3 a_2 i a_3 in let x_2 : Z := to_uint16 (i_8 - i_3) in let x_3 : Z := to_uint16 (i_10 - i_6) in let a_8 : addr := shift a_5 (3%Z + i_3 + i_7) in let a_9 : addr := shift a_5 (2%Z + i_3 + i_7) in let x_4 : Z := i_6 + i_11 in let x_5 : Z := 2147483648%Z + i_10 in let x_6 : Z := 2147483647%Z + i_6 in let a_10 : addr := shift a_7 2%Z in let a_11 : addr := shift a_5 (i_3 + i_7) in ¬ i_3 = 0%Z -> ¬ i_4 = 0%Z -> ¬ i_8 = 0%Z -> ¬ Mk_addr 0%Z 0%Z = a_5 -> ¬ a_6 = Mk_addr 0%Z 0%Z -> ¬ a_7 = Mk_addr 0%Z 0%Z -> 0%Z ≤ i_3 -> 0%Z ≤ i_4 -> i_7 ≤ i_4 -> i_8 ≤ i_4 -> 0%Z ≤ i_5 -> 0%Z ≤ i_8 -> i_3 ≤ i_8 -> x ≤ i_4 -> region (base a_1) ≤ 0%Z -> region (base a_3) ≤ 0%Z -> region (base a_4) ≤ 0%Z -> region (base a_5) ≤ 0%Z -> 2%Z ≤ i_7 -> 3%Z ≤ i_3 -> i_5 ≤ 28%Z -> - 2147483648%Z ≤ x -> x ≤ 2147483647%Z -> i_3 ≤ 2147483648%Z + i_8 -> i_4 ≤ 2147483647%Z + i_7 -> i_7 ≤ 2147483648%Z + i_4 -> i_8 ≤ 2147483647%Z + i_3 -> framed t_4 -> linked t_1 -> is_uint16 i_1 -> is_uint16 i_3 -> is_uint16 i_4 -> is_uint16 i_6 -> is_uint16 i_7 -> is_uint16 i_8 -> is_uint16 i_9 -> is_uint16 i_10 -> is_uint16 i_11 -> is_sint32 i_2 -> valid_rw t_1 a_1 1%Z -> valid_rw t_1 a_3 1%Z -> valid_rw t_1 a_4 15%Z -> is_uint16 x_1 -> valid_rw t_1 (shift a_1 0%Z) 29%Z -> (if decide (i_2 = 0%Z) then i_1 = 3%Z ∧ ¬ i_10 = 0%Z ∧ to_uint16 (i_9 - 3%Z) = i_10 ∧ x_2 = i_9 ∧ x_3 = i_11 ∧ ¬ a_8 = Mk_addr 0%Z 0%Z ∧ ¬ t_2 a_9 = 0%Z ∧ i_6 ≤ i_10 ∧ i_11 ≤ i_10 ∧ x_4 ≤ i_10 ∧ 2%Z ≤ i_6 ∧ i_6 ≤ x_5 ∧ i_10 ≤ x_6 ∧ valid_rw t a_2 1%Z ∧ valid_rd t_1 a_9 1%Z ∧ valid_rd t_1 a_10 1%Z ∧ (0%Z < i_10 -> valid_rd t_1 a_8 i_10) else ¬ i_10 = 0%Z ∧ ¬ a_11 = Mk_addr 0%Z 0%Z ∧ x_2 = i_10 ∧ x_3 = i_11 ∧ i_6 ≤ i_10 ∧ i_11 ≤ i_10 ∧ x_4 ≤ i_10 ∧ 2%Z ≤ i_6 ∧ i_6 ≤ x_5 ∧ i_10 ≤ x_6 ∧ valid_rw t a_2 1%Z ∧ valid_rd t_1 a_10 1%Z ∧ (0%Z < i_10 -> valid_rd t_1 a_11 i_10)) -> (a_11 = Mk_addr 0%Z 0%Z -> i_2 < 0%Z) -> (x_2 = 0%Z -> i_2 < 0%Z) -> (i_2 = 0%Z -> i_1 ≤ x_2) -> (0%Z < i_4 -> valid_rd t_1 (shift a_5 0%Z) i_4) -> (0%Z < i_3 -> valid_rd t_1 a_6 i_3) -> (0%Z < i_8 -> valid_rd t_1 a_6 i_8) -> (¬ a_11 = Mk_addr 0%Z 0%Z -> 0%Z < x_2 -> valid_rd t_1 a_11 x_2) -> i_2 = 0%Z ∨ i_2 < 0%Z -> 0%Z < x_1 ∧ x_1 ≤ i_4.
Admitted.
