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 should_we_balance.A_thread_variables_properties.A_thread_variables_properties.
Require Import should_we_balance.Compound.Compound.
Require Import Why3.Cint.Cint.
Require Import should_we_balance.A_schedule_cpumask.A_schedule_cpumask.
Require Import Why3.Cbits.Cbits.
Open Scope Z_scope.
Theorem goal20 (i_6 : Z) (a_1 : addr) (t_3 : addr -> Z) (t_5 : addr -> addr) (a : addr) (i : Z) (t_2 : addr -> Z) (t_1 : addr -> Z) (i_1 : Z) (i_7 : Z) (i_3 : Z) (i_4 : Z) (i_5 : Z) (t : Z -> Z) (i_2 : Z) (p : bool) (t_4 : addr -> Z) : let x : Z := l_idle_cpu i_6 in let a_2 : addr := shift a_1 3%Z in let x_1 : Z := t_3 a_2 in let a_3 : addr := shift a_1 4%Z in let a_4 : addr := t_5 a_3 in let a_5 : addr := shift a_4 0%Z in let a_6 : addr := t_5 a_5 in let a_7 : addr := shift a_1 1%Z in let x_2 : Z := t_3 a_7 in let x_3 : Z := t_3 (shift a_6 x_2) in let a_8 : addr := shift a i in let a_9 : addr := shift a_8 0%Z in let a_10 : addr := t_5 a_9 in let a_11 : addr := shift a_10 0%Z in let a_12 : addr -> Z := havoc t_2 t_3 a_11 l_size in let a_13 : addr := shift a_1 0%Z in let a_14 : addr := t_5 a_13 in let a_15 : addr := shift a_14 0%Z in let a_16 : addr := t_5 a_15 in let a_17 : addr := l_group_balance_mask a_16 in let a_18 : addr := t_5 (shift a_17 0%Z) in let a_19 : addr := shift a_14 1%Z in let a_20 : addr := shift a_6 0%Z in let a_21 : addr -> Z := havoc t_1 t_3 a_11 l_size in let a_22 : Z := a_12 (shift a_10 i_6) in let a_23 : Z := a_12 (shift a_6 i_1) in let a_24 : Z := a_12 (shift a_6 i_6) in let a_25 : Z := a_12 (shift a_18 i_1) in let a_26 : Z := a_12 a_19 in let a_27 : addr := shift a_18 0%Z in let x_4 : Z := to_uint32 i_7 in ¬ i_3 = - 1%Z -> (¬ x = 0%Z) = (¬ i_4 = 0%Z) -> ¬ x_1 = 2%Z -> ¬ x_3 = 0%Z -> ¬ a_12 (shift a_6 i_5) = 0%Z -> ¬ a_12 (shift a_18 i_5) = 0%Z -> 0%Z ≤ i -> i < l_size -> 0%Z ≤ i_5 -> i_5 < i_3 -> i_5 < l_size -> 0%Z ≤ i_6 -> i_6 < l_size -> 0%Z ≤ i_7 -> i_7 ≤ l_size -> to_uint32 i_6 < l_size -> 0%Z ≤ x_2 -> x_2 < l_size -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> framed t_5 -> linked t -> is_uint8 i_4 -> is_uint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> is_sint32 i_3 -> is_sint32 i_6 -> is_sint32 i_7 -> valid_rd t a_1 5%Z -> is_uint32 x_1 -> is_sint32 x_2 -> valid_rd t a_3 1%Z -> valid_rd t a_7 1%Z -> valid_rd t a_2 1%Z -> valid_rd t a_13 1%Z -> valid_rd t a_8 1%Z -> valid_rd t a_4 1%Z -> valid_rd t (t_5 (shift a_1 2%Z)) 2%Z -> valid_rd t a_14 2%Z -> is_sint32 (t_3 a_19) -> valid_rd t a_9 1%Z -> valid_rd t a_5 1%Z -> valid_rd t a_15 1%Z -> valid_rd t a_16 1%Z -> valid_rd t a_17 1%Z -> is_uint8 x_3 -> valid_rd t a_11 l_size -> valid_rd t a_20 l_size -> valid_rw t a_11 l_size -> is_uint8 (a_21 (shift a_6 (- 1%Z))) -> is_uint8 (a_21 (shift a_18 (- 1%Z))) -> is_uint8 a_22 -> is_uint8 a_23 -> is_uint8 (a_12 (shift a_6 i_3)) -> is_uint8 a_24 -> is_uint8 a_25 -> is_uint8 (a_12 (shift a_18 i_3)) -> is_sint32 (a_21 a_19) -> is_sint32 a_26 -> valid_rd t a_27 l_size -> separated a_11 l_size a_27 l_size -> (if decide (i_4 = 0%Z) then i_3 = i_1 ∧ i_6 ≤ 2147483646%Z else p = false ∧ i_2 = i_1 ∧ ¬ x = 0%Z ∧ land 7%Z (t_4 a_19) = 0%Z ∧ a_12 = t_4 ∧ i_6 ≤ 2147483646%Z ∧ ¬ p_idle_core t_5 t_4 i_6 ∧ valid_rd t a_19 1%Z ∧ (if decide (i_2 = - 1%Z) then i_6 = i_3 else i_3 = i_2)) -> (¬ land 7%Z a_26 = 0%Z -> i_1 = - 1%Z) -> (¬ i_1 = - 1%Z -> ¬ l_idle_cpu i_1 = 0%Z ∧ ¬ a_23 = 0%Z ∧ ¬ a_25 = 0%Z ∧ 0%Z ≤ i_1 ∧ i_1 < l_size) -> (i_1 = - 1%Z -> (∀(i_8 : Z), ¬ a_12 (shift a_18 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_12 (shift a_10 i_8) = 0%Z)) -> ((∃(i_8 : Z), ¬ a_12 (shift a_10 i_8) = 0%Z ∧ ¬ a_12 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_4 ≤ i_8) -> x_4 ≤ i_6) -> ((∃(i_8 : Z), ¬ a_12 (shift a_10 i_8) = 0%Z ∧ ¬ a_12 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_4 ≤ i_8) -> ¬ a_22 = 0%Z ∧ ¬ a_24 = 0%Z) -> ((∀(i_8 : Z), i_8 < l_size -> x_4 ≤ i_8 -> a_12 (shift a_10 i_8) = 0%Z ∨ a_12 (shift a_6 i_8) = 0%Z) -> l_size = i_6) -> (¬ i_1 = - 1%Z -> (∀(i_8 : Z), ¬ a_12 (shift a_6 i_8) = 0%Z -> ¬ a_12 (shift a_18 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < i_1 -> i_8 < l_size -> l_idle_cpu i_8 = 0%Z)) -> (i_1 = - 1%Z -> (∀(i_8 : Z), ¬ a_12 (shift a_6 i_8) = 0%Z -> ¬ a_12 (shift a_18 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < i_7 -> i_8 < l_size -> l_idle_cpu i_8 = 0%Z)) -> ((∃(i_8 : Z), ¬ a_12 (shift a_10 i_8) = 0%Z ∧ ¬ a_12 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_4 ≤ i_8) -> (∀(i_8 : Z), i_8 < i_6 -> x_4 ≤ i_8 -> a_12 (shift a_10 i_8) = 0%Z ∨ a_12 (shift a_6 i_8) = 0%Z)) -> (¬ i_1 = - 1%Z -> (∀(i_8 : Z), ¬ a_12 (shift a_6 i_8) = 0%Z -> ¬ a_12 (shift a_18 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_1 ≤ i_8 -> i_8 < i_7 -> i_8 < l_size -> ¬ p_idle_core t_5 a_12 i_8)) -> (¬ i_1 = - 1%Z -> (∀(i_8 : Z), ¬ a_12 (shift a_18 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_12 (shift a_10 i_8) = 0%Z ∨ ¬ p_idle_core t_5 a_12 i_8)) -> i_4 = 0%Z ∨ i_4 = 1%Z -> (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_20 l_size (shift (t_5 (shift (shift a i_8) 0%Z)) 0%Z) l_size) -> (∀(i_8 : Z), let a_28 : addr := shift a i_8 in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t a_28 1%Z ∧ valid_rw t (shift (t_5 (shift a_28 0%Z)) 0%Z) l_size) -> (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> (¬ a_21 (shift a_18 i_8) = 0%Z) = (¬ a_21 (shift a_10 i_8) = 0%Z)) -> (∀(i_8 : Z), ¬ a_12 (shift a_10 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_12 (shift a_18 i_8) = 0%Z) -> (∀(a_28 : addr), let a_29 : addr := l_sched_group_cpus a_28 in let a_30 : addr := shift (t_5 (shift a_29 0%Z)) 0%Z in valid_rd t a_29 1%Z ∧ valid_rd t a_30 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_30 l_size (shift (t_5 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(a_28 : addr), let a_29 : addr := l_sched_group_mask a_28 in let a_30 : addr := shift (t_5 (shift a_29 0%Z)) 0%Z in valid_rd t a_29 1%Z ∧ valid_rd t a_30 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_30 l_size (shift (t_5 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(a_28 : addr), let a_29 : addr := l_group_balance_mask a_28 in let a_30 : addr := shift (t_5 (shift a_29 0%Z)) 0%Z in valid_rd t a_29 1%Z ∧ valid_rd t a_30 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_30 l_size (shift (t_5 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(i_8 : Z), let a_28 : addr := l_cpu_smt_mask i_8 in let a_29 : addr := shift (t_5 (shift a_28 0%Z)) 0%Z in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t a_28 1%Z ∧ valid_rd t a_29 l_size ∧ (∀(i_9 : Z), 0%Z ≤ i_9 -> i_9 < l_size -> separated a_29 l_size (shift (t_5 (shift (shift a i_9) 0%Z)) 0%Z) l_size)) -> l_idle_cpu i_5 = 0%Z.
Admitted.
