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Proof step 35 from proof int2bytes-last-01 (previous step)

0 < i % 256, 127 < i % 256, 0 ≤ i, 0 < i, 256 ≤ i ⊦ int2bytes(i % 256).last = i2b(i), ~256 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 37:
127 < i % 256 ∧ i % 256 ≤ 255, 0 < i % 256, 127 < i % 256, 0 ≤ i, 0 < i, 256 ≤ i ⊦ (i2b(0) ' + i2b(i % 256 - 256) ').last = i2b(i), ~256 = i

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i % 256]

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ 255 < i % 256; Used terms: i % 256