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Proof step 44 from proof int2bytes-first-zerobyte (previous step)

0 < i, 0 ≤ i, 256 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → (int2bytes(i0).first = i2b(0) ↔ n→i(# int2bits(i0)) % 8 = 1) ⊦ fillsgn(9, int2bits(i % 256)) = [], int2bytes(i / 256).first = i2b(0) ↔ (n→i(# fillsgn(9, int2bits(i % 256)) - 1) + n→i(# int2bits(i / 256))) % 8 = 1, n→i(# fillsgn(9, int2bits(i % 256)) - 1) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 46:
¬ # int2bits(i % 256) ≤ 9, 0 < i, 0 ≤ i, 256 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → (int2bytes(i0).first = i2b(0) ↔ n→i(# int2bits(i0)) % 8 = 1) ⊦ fillsgn(9, int2bits(i % 256)) = [], int2bytes(i / 256).first = i2b(0) ↔ (n→i(# fillsgn(9, int2bits(i % 256)) - 1) + n→i(# int2bits(i / 256))) % 8 = 1, n→i(# fillsgn(9, int2bits(i % 256)) - 1) % 8 = 0

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(i % 256), 9] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: int2bits(i % 256), 9