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 int32_quat_comp_norm_shortest.Compound.Compound.
Require Import int32_quat_comp_norm_shortest.Axiomatic15.Axiomatic15.
Require Import int32_quat_comp_norm_shortest.S8_Int32Quat.S8_Int32Quat.
Open Scope Z_scope.
Theorem goal5 (i : s8_int32quat) (t_1 : addr -> Z) (a : addr) (a_1 : addr) (i_1 : s8_int32quat) (t : Z -> Z) : let x : Z := f8_int32quat_qi i in let x_1 : Z := f8_int32quat_qx i in let x_2 : Z := f8_int32quat_qy i in let x_3 : Z := f8_int32quat_qz i in let x_4 : Z := t_1 (shift a 0%Z) in let x_5 : Z := t_1 (shift a_1 0%Z) in let x_6 : Z := t_1 (shift a 1%Z) in let x_7 : Z := t_1 (shift a_1 1%Z) in let x_8 : Z := t_1 (shift a 2%Z) in let x_9 : Z := t_1 (shift a_1 2%Z) in let x_10 : Z := t_1 (shift a 3%Z) in let x_11 : Z := t_1 (shift a_1 3%Z) in let x_12 : Z := f8_int32quat_qi i_1 in let x_13 : Z := f8_int32quat_qx i_1 in let x_14 : Z := f8_int32quat_qy i_1 in let x_15 : Z := f8_int32quat_qz i_1 in region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> - 2147483647%Z ≤ x -> - 2147483647%Z ≤ x_1 -> - 2147483647%Z ≤ x_2 -> - 2147483647%Z ≤ x_3 -> x ≤ 2147483647%Z -> x_1 ≤ 2147483647%Z -> x_2 ≤ 2147483647%Z -> x_3 ≤ 2147483647%Z -> - 23170%Z ≤ x_4 -> - 23170%Z ≤ x_5 -> - 23170%Z ≤ x_6 -> - 23170%Z ≤ x_7 -> - 23170%Z ≤ x_8 -> - 23170%Z ≤ x_9 -> - 23170%Z ≤ x_10 -> - 23170%Z ≤ x_11 -> x_4 ≤ 23170%Z -> x_5 ≤ 23170%Z -> x_6 ≤ 23170%Z -> x_7 ≤ 23170%Z -> x_8 ≤ 23170%Z -> x_9 ≤ 23170%Z -> x_10 ≤ 23170%Z -> x_11 ≤ 23170%Z -> linked t -> is_sint32 x -> is_sint32 x_1 -> is_sint32 x_2 -> is_sint32 x_3 -> is_sint32 x_12 -> is_sint32 x_13 -> is_sint32 x_14 -> is_sint32 x_15 -> valid_rd t a 4%Z -> valid_rd t a_1 4%Z -> separated a_1 4%Z a 4%Z -> is_sint32 x_4 -> is_sint32 x_5 -> is_sint32 x_6 -> is_sint32 x_7 -> is_sint32 x_8 -> is_sint32 x_9 -> is_sint32 x_10 -> is_sint32 x_11 -> p_rvalid_bound_int32quat t t_1 a 13777%Z -> p_rvalid_bound_int32quat t t_1 a_1 13777%Z -> (p_bound_int32quat t_1 a 23170%Z -> p_bound_int32quat t_1 a_1 23170%Z -> - 65535%Z ≤ x ∧ x ≤ 65535%Z) -> (p_bound_int32quat t_1 a 23170%Z -> p_bound_int32quat t_1 a_1 23170%Z -> - 65535%Z ≤ x_1 ∧ x_1 ≤ 65535%Z) -> (p_bound_int32quat t_1 a 23170%Z -> p_bound_int32quat t_1 a_1 23170%Z -> - 65535%Z ≤ x_2 ∧ x_2 ≤ 65535%Z) -> (p_bound_int32quat t_1 a 23170%Z -> p_bound_int32quat t_1 a_1 23170%Z -> - 65535%Z ≤ x_3 ∧ x_3 ≤ 65535%Z) -> (p_bound_int32quat t_1 a 13777%Z -> p_bound_int32quat t_1 a_1 13777%Z -> - 23170%Z ≤ x ∧ x ≤ 23170%Z) -> (p_bound_int32quat t_1 a 13777%Z -> p_bound_int32quat t_1 a_1 13777%Z -> - 23170%Z ≤ x_1 ∧ x_1 ≤ 23170%Z) -> (p_bound_int32quat t_1 a 13777%Z -> p_bound_int32quat t_1 a_1 13777%Z -> - 23170%Z ≤ x_2 ∧ x_2 ≤ 23170%Z) -> (p_bound_int32quat t_1 a 13777%Z -> p_bound_int32quat t_1 a_1 13777%Z -> - 23170%Z ≤ x_3 ∧ x_3 ≤ 23170%Z) -> x_12 = x ∨ x + x_12 = 0%Z -> x_13 = x_1 ∨ x_1 + x_13 = 0%Z -> x_14 = x_2 ∨ x_2 + x_14 = 0%Z -> x_15 = x_3 ∨ x_3 + x_15 = 0%Z -> - 23170%Z ≤ x_12 ∧ - 23170%Z ≤ x_13 ∧ - 23170%Z ≤ x_14 ∧ - 23170%Z ≤ x_15 ∧ x_12 ≤ 23170%Z ∧ x_13 ≤ 23170%Z ∧ x_14 ≤ 23170%Z ∧ x_15 ≤ 23170%Z.
Admitted.
