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Proof step 9 from proof int2bytes-first-zerobyte (previous step)

0 < i, 127 < i, i ≤ 255, 0 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → (int2bytes(i0).first = i2b(0) ↔ n→i(# int2bits(i0)) % 8 = 1) ⊦ int2bytes(i).first = i2b(0) ↔ n→i(# int2bits(i)) % 8 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 11:
127 < i ∧ i ≤ 255, 0 < i, 127 < i, i ≤ 255, 0 ≤ i, ∀ i0. i→n(i0) < i→n(i) → 0 ≤ i0 → (int2bytes(i0).first = i2b(0) ↔ n→i(# int2bits(i0)) % 8 = 1) ⊦ (i2b(0) ' + i2b(i - 256) ').first = i2b(0) ↔ n→i(# int2bits(i)) % 8 = 1

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0); Used terms: i