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 goal41 (a_1 : addr) (t_7 : addr -> Z) (t_8 : addr -> addr) (a : addr) (i : Z) (t_6 : addr -> Z) (i_5 : Z) (i_2 : Z) (i_6 : Z) (t_5 : addr -> Z) (t : Z -> Z) (i_1 : Z) (i_3 : Z) (i_4 : Z) (i_7 : Z) (t_4 : Z -> Z) (t_1 : Z -> Z) (t_2 : Z -> Z) (t_3 : Z -> Z) : let a_2 : addr := shift a_1 3%Z in let x : Z := t_7 a_2 in let a_3 : addr := shift a_1 4%Z in let a_4 : addr := t_8 a_3 in let a_5 : addr := shift a_4 0%Z in let a_6 : addr := t_8 a_5 in let a_7 : addr := shift a_1 1%Z in let x_1 : Z := t_7 a_7 in let x_2 : Z := t_7 (shift a_6 x_1) in let a_8 : addr := shift a_1 0%Z in let a_9 : addr := shift a i in let a_10 : addr := t_8 a_8 in let a_11 : addr := shift a_9 0%Z in let a_12 : addr := shift a_10 0%Z in let a_13 : addr := t_8 a_12 in let a_14 : addr := l_group_balance_mask a_13 in let a_15 : addr := t_8 a_11 in let a_16 : addr := shift a_15 0%Z in let a_17 : addr := shift a_6 0%Z in let a_18 : addr -> Z := havoc t_6 t_7 a_16 l_size in let a_19 : Z := a_18 (shift a_15 i_5) in let a_20 : Z := a_18 (shift a_6 i_2) in let a_21 : Z := a_18 (shift a_6 i_5) in let a_22 : addr := t_8 (shift a_14 0%Z) in let a_23 : Z := a_18 (shift a_22 i_2) in let a_24 : Z := a_18 a_7 in let a_25 : addr := shift a_10 1%Z in let a_26 : Z := a_18 a_25 in let a_27 : addr := shift a_22 0%Z in let x_3 : Z := land 7%Z a_26 in let x_4 : Z := l_group_balance_cpu a_13 in let x_5 : Z := to_uint32 i_6 in let a_28 : addr -> Z := havoc t_5 t_7 a_16 l_size in ¬ x = 2%Z -> ¬ x_2 = 0%Z -> 0%Z ≤ i -> i < l_size -> 0%Z ≤ i_6 -> i_6 ≤ l_size -> 0%Z ≤ x_1 -> x_1 < l_size -> region (base a) ≤ 0%Z -> region (base a_1) ≤ 0%Z -> framed t_8 -> linked t -> is_uint32 i -> is_sint32 i_1 -> is_sint32 i_2 -> is_sint32 i_3 -> is_sint32 i_4 -> is_sint32 i_5 -> is_sint32 i_6 -> is_sint32 i_7 -> valid_rd t a_1 5%Z -> is_uint32 x -> is_sint32 x_1 -> 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_8 1%Z -> valid_rd t a_9 1%Z -> valid_rd t a_4 1%Z -> valid_rd t (t_8 (shift a_1 2%Z)) 2%Z -> valid_rd t a_10 2%Z -> valid_rd t a_11 1%Z -> valid_rd t a_5 1%Z -> valid_rd t a_12 1%Z -> valid_rd t a_13 1%Z -> valid_rd t a_14 1%Z -> is_uint8 x_2 -> valid_rd t a_16 l_size -> valid_rd t a_17 l_size -> valid_rw t a_16 l_size -> is_uint8 a_19 -> is_uint8 a_20 -> is_uint8 a_21 -> is_uint8 a_23 -> is_sint32 a_24 -> is_sint32 a_26 -> valid_rd t a_27 l_size -> separated a_16 l_size a_27 l_size -> (if decide (to_uint32 i_5 < l_size) then i_7 = i_5 ∧ t_4 = t ∧ ¬ l_idle_cpu i_7 = 0%Z ∧ (if decide (a_24 = i_7) then 1%Z else 0%Z) = i_1 ∧ 0%Z ≤ i_7 ∧ i_7 < l_size ∧ valid_rd t_4 a_7 1%Z ∧ valid_rd t_4 a_8 1%Z ∧ valid_rd t_4 a_25 1%Z ∧ (¬ x_3 = 0%Z ∨ p_idle_core t_8 a_18 i_7 ∧ (∀(i_8 : Z), let a_29 : addr := shift a i_8 in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t_4 a_29 1%Z ∧ valid_rw t_4 (shift (t_8 (shift a_29 0%Z)) 0%Z) l_size) ∧ (∀(a_29 : addr), let a_30 : addr := l_sched_group_cpus a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t_4 a_30 1%Z ∧ valid_rd t_4 a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) ∧ (∀(a_29 : addr), let a_30 : addr := l_sched_group_mask a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t_4 a_30 1%Z ∧ valid_rd t_4 a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) ∧ (∀(a_29 : addr), let a_30 : addr := l_group_balance_mask a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t_4 a_30 1%Z ∧ valid_rd t_4 a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) ∧ (∀(i_8 : Z), let a_29 : addr := l_cpu_smt_mask i_8 in let a_30 : addr := shift (t_8 (shift a_29 0%Z)) 0%Z in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t_4 a_29 1%Z ∧ valid_rd t_4 a_30 l_size ∧ (∀(i_9 : Z), 0%Z ≤ i_9 -> i_9 < l_size -> separated a_30 l_size (shift (t_8 (shift (shift a i_9) 0%Z)) 0%Z) l_size))) else i_3 = i_2 ∧ t_1 = t ∧ (if decide (i_3 = - 1%Z) then t_2 = t_1 ∧ x_4 = i_4 ∧ (if decide (a_24 = i_4) then 1%Z else 0%Z) = i_1 ∧ valid_rd t_2 a_7 1%Z else t_3 = t_1 ∧ (if decide (a_24 = i_3) then 1%Z else 0%Z) = i_1 ∧ valid_rd t_3 a_7 1%Z)) -> (¬ x_3 = 0%Z -> i_2 = - 1%Z) -> (¬ i_2 = - 1%Z -> ¬ l_idle_cpu i_2 = 0%Z ∧ ¬ a_20 = 0%Z ∧ ¬ a_23 = 0%Z ∧ 0%Z ≤ i_2 ∧ i_2 < l_size) -> (i_2 = - 1%Z -> (∀(i_8 : Z), ¬ a_18 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_18 (shift a_15 i_8) = 0%Z)) -> ((∃(i_8 : Z), ¬ a_18 (shift a_15 i_8) = 0%Z ∧ ¬ a_18 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_5 ≤ i_8) -> i_5 < l_size) -> ((∃(i_8 : Z), ¬ a_18 (shift a_15 i_8) = 0%Z ∧ ¬ a_18 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_5 ≤ i_8) -> i_5 < l_size ∧ x_5 ≤ i_5) -> ((∃(i_8 : Z), ¬ a_18 (shift a_15 i_8) = 0%Z ∧ ¬ a_18 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_5 ≤ i_8) -> ¬ a_19 = 0%Z ∧ ¬ a_21 = 0%Z) -> ((∀(i_8 : Z), i_8 < l_size -> x_5 ≤ i_8 -> a_18 (shift a_15 i_8) = 0%Z ∨ a_18 (shift a_6 i_8) = 0%Z) -> l_size = i_5) -> (¬ i_2 = - 1%Z -> (∀(i_8 : Z), ¬ a_18 (shift a_6 i_8) = 0%Z -> ¬ a_18 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < i_2 -> i_8 < l_size -> l_idle_cpu i_8 = 0%Z)) -> (i_2 = - 1%Z -> (∀(i_8 : Z), ¬ a_18 (shift a_6 i_8) = 0%Z -> ¬ a_18 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < i_6 -> i_8 < l_size -> l_idle_cpu i_8 = 0%Z)) -> ((∃(i_8 : Z), ¬ a_18 (shift a_15 i_8) = 0%Z ∧ ¬ a_18 (shift a_6 i_8) = 0%Z ∧ i_8 < l_size ∧ x_5 ≤ i_8) -> (∀(i_8 : Z), i_8 < i_5 -> x_5 ≤ i_8 -> a_18 (shift a_15 i_8) = 0%Z ∨ a_18 (shift a_6 i_8) = 0%Z)) -> (¬ i_2 = - 1%Z -> (∀(i_8 : Z), ¬ a_18 (shift a_6 i_8) = 0%Z -> ¬ a_18 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_2 ≤ i_8 -> i_8 < i_6 -> i_8 < l_size -> ¬ p_idle_core t_8 a_18 i_8)) -> (¬ i_2 = - 1%Z -> (∀(i_8 : Z), ¬ a_18 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_18 (shift a_15 i_8) = 0%Z ∨ ¬ p_idle_core t_8 a_18 i_8)) -> (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_17 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size) -> (∀(i_8 : Z), let a_29 : addr := shift a i_8 in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t a_29 1%Z ∧ valid_rw t (shift (t_8 (shift a_29 0%Z)) 0%Z) l_size) -> (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> (¬ a_28 (shift a_22 i_8) = 0%Z) = (¬ a_28 (shift a_15 i_8) = 0%Z)) -> (∀(i_8 : Z), ¬ a_18 (shift a_15 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> ¬ a_18 (shift a_22 i_8) = 0%Z) -> (∀(i_8 : Z), ¬ t_7 (shift a_6 i_8) = 0%Z -> ¬ t_7 (shift a_22 i_8) = 0%Z -> 0%Z ≤ i_8 -> i_8 < l_size -> l_idle_cpu i_8 = 0%Z) -> (∀(a_29 : addr), let a_30 : addr := l_sched_group_cpus a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t a_30 1%Z ∧ valid_rd t a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(a_29 : addr), let a_30 : addr := l_sched_group_mask a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t a_30 1%Z ∧ valid_rd t a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(a_29 : addr), let a_30 : addr := l_group_balance_mask a_29 in let a_31 : addr := shift (t_8 (shift a_30 0%Z)) 0%Z in valid_rd t a_30 1%Z ∧ valid_rd t a_31 l_size ∧ (∀(i_8 : Z), 0%Z ≤ i_8 -> i_8 < l_size -> separated a_31 l_size (shift (t_8 (shift (shift a i_8) 0%Z)) 0%Z) l_size)) -> (∀(i_8 : Z), let a_29 : addr := l_cpu_smt_mask i_8 in let a_30 : addr := shift (t_8 (shift a_29 0%Z)) 0%Z in 0%Z ≤ i_8 -> i_8 < l_size -> valid_rd t a_29 1%Z ∧ valid_rd t a_30 l_size ∧ (∀(i_9 : Z), 0%Z ≤ i_9 -> i_9 < l_size -> separated a_30 l_size (shift (t_8 (shift (shift a i_9) 0%Z)) 0%Z) l_size)) -> (x_1 = x_4) = (¬ i_1 = 0%Z).
Admitted.
