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 goal11 (a_2 : addr) (a : addr) (i_7 : Z) (i_10 : Z) (i_8 : Z) (i_9 : Z) (a_1 : addr) (i_4 : Z) (i_1 : Z) (t : Z -> Z) (i : Z) (i_2 : Z) (i_3 : Z) (i_11 : Z) (i_5 : Z) (i_6 : Z) (p : bool) : let x : Z := base a_2 in let x_1 : Z := base a in let x_2 : Z := i_7 - i_10 in let x_3 : Z := i_8 + i_9 in let x_4 : Z := to_sint32 x_3 in let a_3 : addr := shift a_1 i_4 in let a_4 : addr := shift a_2 i_10 in ¬ i_7 = 0%Z -> ¬ Mk_addr 0%Z 0%Z = a_2 -> ¬ x = x_1 -> 0%Z ≤ i_1 -> 0%Z ≤ i_7 -> i_10 ≤ i_7 -> 0%Z ≤ i_10 -> region x_1 ≤ 0%Z -> region x ≤ 0%Z -> - 2147483648%Z ≤ i_7 -> 2%Z ≤ i_10 -> i_7 ≤ 2147483647%Z -> linked t -> is_uint16 i -> is_uint16 i_1 -> is_uint16 i_2 -> is_uint16 i_3 -> is_uint16 i_4 -> is_uint16 i_7 -> is_uint16 i_8 -> is_uint16 i_9 -> is_uint16 i_10 -> is_uint16 i_11 -> is_sint32 i_5 -> is_sint32 i_6 -> valid_rw t a 15%Z -> is_uint16 x_2 -> (if decide (i_5 = 0%Z) then ¬ i_9 = 0%Z ∧ i + i_10 = i_7 ∧ to_uint16 (i - i_8 - i_9) = i_1 ∧ shift a_2 (i_7 + i_8 + i_9 - i) = a_1 ∧ - 2147483648%Z ≤ x_3 ∧ x_3 ≤ 2147483647%Z ∧ x_4 ≤ 2147483648%Z + i ∧ i ≤ 2147483647%Z + x_4 else i_1 + i_10 = i_7 ∧ shift a_2 (i_7 - i_1) = a_1) -> (if decide (i_6 = 0%Z) then p = false ∧ i_2 = i_1 ∧ ¬ i_3 = 0%Z ∧ ¬ a_3 = Mk_addr 0%Z 0%Z ∧ to_uint16 (i_2 - i_4) = i_3 ∧ to_uint16 (i_3 - i_11) = 0%Z ∧ i_11 ≤ i_3 ∧ i_2 ≤ 2147483647%Z + i_4 ∧ i_3 ≤ 2147483647%Z + i_11 ∧ i_4 ≤ 2147483648%Z + i_2 ∧ i_11 ≤ 2147483648%Z + i_3 ∧ (0%Z < i_3 -> valid_rd t a_3 i_3) else i_1 = 0%Z) -> (i_10 = i_7 -> i_5 < 0%Z) -> (i_1 = 0%Z -> i_6 < 0%Z) -> (Mk_addr 0%Z 0%Z = a_1 -> i_6 < 0%Z) -> (a_4 = Mk_addr 0%Z 0%Z -> i_5 < 0%Z) -> (i_5 = 0%Z -> i_9 + i_10 ≤ i_7) -> (i_6 = 0%Z -> i_4 ≤ i_1 ∧ 2%Z ≤ i_4) -> (i_5 = 0%Z -> i_8 + i_9 + i_10 ≤ i_7) -> (0%Z < i_7 -> valid_rd t (shift a_2 0%Z) i_7) -> (i_5 = 0%Z -> i_8 + i_10 ≤ i_7 ∧ 2%Z ≤ i_8) -> (¬ Mk_addr 0%Z 0%Z = a_1 -> 0%Z < i_1 -> valid_rd t (shift a_1 0%Z) i_1) -> (¬ a_4 = Mk_addr 0%Z 0%Z -> i_10 < i_7 -> valid_rd t a_4 x_2) -> i_5 = 0%Z ∨ i_5 < 0%Z -> i_6 = 0%Z ∨ i_6 < 0%Z -> valid_rw t (shift a 13%Z) 1%Z.
Admitted.
