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Proof step 41 from proof int2bytes-leading-zeros (previous step)

int2bytes(i / 256) = i2b(0) ', int2bytes(i % 256) = bytes0 + i2b(0) ', i2b(0) ∈ int2bytes(i % 256), 0 < i, 0 ≤ i, 255 < i, i / 256 ≤ 127, ∀ bytes, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + i2b(0) ' + bytes ∧ 0 ≤ i0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
0 ≤ i, i ≤ 127 ⊦ int2bytes(i) = i2b(i) '
Proof step 43:
0 ≤ i / 256 ∧ i / 256 ≤ 127, i2b(i / 256) ' = i2b(0) ', int2bytes(i % 256) = bytes0 + i2b(0) ', i2b(0) ∈ int2bytes(i % 256), 0 < i, 0 ≤ i, 255 < i, i / 256 ≤ 127, ∀ bytes, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + i2b(0) ' + bytes ∧ 0 ≤ i0 → false ⊦

Rule argument

name: int2bytes-le127 rotate: F subst: [i] → [i / 256]

Additional information

Used simplifier rules: ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i / j;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); Used terms: i / 256