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Require Import Lia ZArith.
Open Scope Z_scope.
Unset Lia Cache.
Goal forall Y r0 r q q0 r1 q1 : Z,
3 = 4294967296 * q1 + r1 ->
Y - r1 = 4294967296 * q0 + r0 ->
r1 < 4294967296 ->
0 <= r1 ->
r0 < 4294967296 ->
0 <= r0 ->
r < 4 ->
0 <= r ->
0 < 4 ->
r0 = 4 * q + r ->
Y < 4294967296 ->
0 <= Y ->
r = 0 ->
r0 < 268517376 ->
268513280 <= r0 ->
268587008 <= Y ->
False.
Proof.
intros.
Time lia. (* used to be 20s *)
Qed.
Goal forall Y r0 r q q0 r1 q1 : Z,
3 = 4294967296 * q1 + r1 ->
Y - r1 = 4294967296 * q0 + r0 ->
r1 < 4294967296 ->
0 <= r1 ->
r0 < 4294967296 ->
0 <= r0 ->
r < 4 ->
0 <= r ->
0 < 4 ->
r0 = 4 * q + r ->
Y < 4294967296 ->
0 <= Y ->
r = 0 ->
r0 < 268517376 ->
268513280 <= r0 ->
268587008 <= Y ->
False.
Proof.
intros.
Time lia. (* used to be 20s *)
Qed.
Goal forall (two64 right left : Z) (length_xs v : nat) (x2 x1 : Z)
(length_x : nat) (r3 r2 q r r1 q0 r0 q1 q2 q3 : Z),
two64 = 2 ^ 64 ->
r3 = 8 * Z.of_nat length_xs ->
r2 = 8 * Z.of_nat length_x ->
0 <= 8 * Z.of_nat length_x ->
8 * Z.of_nat length_x < two64 ->
r1 = 2 ^ 4 * q + r ->
0 < 2 ^ 4 ->
0 <= r ->
r < 2 ^ 4 ->
x1 + q * 2 ^ 3 - x1 = two64 * q0 + r0 ->
0 < two64 ->
0 <= r0 ->
r0 < two64 ->
8 * Z.of_nat length_x = two64 * q1 + r1 ->
0 <= r1 ->
r1 < two64 ->
x2 - x1 = two64 * q2 + r2 ->
0 <= r2 ->
r2 < two64 ->
right - left = two64 * q3 + r3 ->
0 <= r3 ->
r3 < two64 ->
Z.of_nat length_x = Z.of_nat v ->
0 <= Z.of_nat length_x ->
0 <= Z.of_nat length_xs ->
0 <= Z.of_nat v ->
(r2 = 0 -> False) ->
(2 ^ 4 = 0 -> False) ->
(2 ^ 4 < 0 -> False) ->
(two64 = 0 -> False) ->
(two64 < 0 -> False) ->
(r0 < 8 * Z.of_nat length_x -> False) ->
False.
Proof.
intros.
subst.
Time lia.
Qed.
Goal forall (two64 right left : Z) (length_xs v : nat) (x2 x1 : Z)
(length_x : nat) (r3 r2 q r r1 q0 r0 q1 q2 q3 : Z),
two64 = 2 ^ 64 ->
r3 = 8 * Z.of_nat length_xs ->
r2 = 8 * Z.of_nat length_x ->
0 <= 8 * Z.of_nat length_x ->
8 * Z.of_nat length_x < two64 ->
r1 = 2 ^ 4 * q + r ->
0 < 2 ^ 4 ->
0 <= r ->
r < 2 ^ 4 ->
x1 + q * 2 ^ 3 - x1 = two64 * q0 + r0 ->
0 < two64 ->
0 <= r0 ->
r0 < two64 ->
8 * Z.of_nat length_x = two64 * q1 + r1 ->
0 <= r1 ->
r1 < two64 ->
x2 - x1 = two64 * q2 + r2 ->
0 <= r2 ->
r2 < two64 ->
right - left = two64 * q3 + r3 ->
0 <= r3 ->
r3 < two64 ->
Z.of_nat length_x = Z.of_nat v ->
0 <= Z.of_nat length_x ->
0 <= Z.of_nat length_xs ->
0 <= Z.of_nat v ->
(r2 = 0 -> False) ->
(2 ^ 4 = 0 -> False) ->
(2 ^ 4 < 0 -> False) ->
(two64 = 0 -> False) ->
(two64 < 0 -> False) ->
(r0 < 8 * Z.of_nat length_x -> False) ->
False.
Proof.
intros.
Time lia.
Qed.
Require Import Lia ZArith.
Open Scope Z_scope.
Unset Lia Cache.
Axiom word: Type.
Goal forall (right left : Z) (length_xs : nat) (r14 : Z) (v : nat) (x : list word)
(x2 x1 r8 q2 q r q0 r0 r3 r10 r13 q1 r1 r9 r2 r4 q3 q4
r5 q5 r6 q6 r7 q7 q8 q9 q10 r11 q11 r12 q12 q13 q14 z83 z84 : Z),
z84 = 0 ->
Z.of_nat (Datatypes.length x) - (z83 + 1) <= 0 ->
z84 = Z.of_nat (Datatypes.length x) - (z83 + 1) ->
z83 = 0 ->
q0 <= 0 ->
0 <= Z.of_nat v ->
0 <= Z.of_nat length_xs ->
0 <= Z.of_nat (Datatypes.length x) ->
Z.of_nat (Datatypes.length x) = Z.of_nat v ->
r14 < 2 ^ 64 ->
0 <= r14 ->
right - left = 2 ^ 64 * q14 + r14 ->
r13 < 2 ^ 64 ->
0 <= r13 ->
r10 - x1 = 2 ^ 64 * q13 + r13 ->
r12 < 2 ^ 64 ->
0 <= r12 ->
q = 2 ^ 64 * q12 + r12 ->
r11 < 2 ^ 64 ->
0 <= r11 ->
r12 * 2 ^ 3 = 2 ^ 64 * q11 + r11 ->
r10 < 2 ^ 64 ->
0 <= r10 ->
x1 + r11 = 2 ^ 64 * q10 + r10 ->
r9 < 2 ^ 64 ->
0 <= r9 ->
r10 + r3 = 2 ^ 64 * q9 + r9 ->
r8 < 2 ^ 64 ->
0 <= r8 ->
x2 - x1 = 2 ^ 64 * q8 + r8 ->
r7 < 2 ^ 64 ->
0 <= r7 ->
Z.shiftr r8 4 = 2 ^ 64 * q7 + r7 ->
r6 < 2 ^ 64 ->
0 <= r6 ->
Z.shiftl r7 3 = 2 ^ 64 * q6 + r6 ->
r5 < 2 ^ 64 ->
0 <= r5 ->
x1 + r6 = 2 ^ 64 * q5 + r5 ->
r4 < 2 ^ 64 ->
0 <= r4 ->
r5 - x1 = 2 ^ 64 * q4 + r4 ->
r3 < 2 ^ 64 ->
0 <= r3 ->
8 = 2 ^ 64 * q3 + r3 ->
r2 < r3 ->
0 <= r2 ->
r4 = r3 * q2 + r2 ->
r1 < 2 ^ 64 ->
0 <= r1 ->
0 < 2 ^ 64 ->
x2 - r9 = 2 ^ 64 * q1 + r1 ->
r0 < r3 ->
0 <= r0 ->
0 < r3 ->
r13 = r3 * q0 + r0 ->
r < 2 ^ 4 ->
0 <= r ->
0 < 2 ^ 4 ->
r8 = 2 ^ 4 * q + r ->
r8 = 8 * Z.of_nat (Datatypes.length x) ->
r14 = 8 * Z.of_nat length_xs ->
(r1 = 8 * z84 -> False) ->
False.
Proof.
intros.
Time lia.
Qed.
Goal forall (x2 x3 x : Z)
(H : 0 <= 1073741824 * x + x2 - 67146752)
(H0 : 0 <= -8192 + x2)
(H1 : 0 <= 34816 + - x2)
(H2 : 0 <= -1073741824 * x - x2 + 1073741823),
False.
Proof.
intros.
Time Lia.lia.
Qed.
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