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Proof step 5 from proof int2bytes-rec-neg-06 (previous step)

j % 2 ^ (i * 8) = 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ int2bytes(j) = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
j < ~(2 ^ (i * 8 - 1)), 0 < i, j % 2 ^ (i * 8) = 0 ⊦ int2bytes(j) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i + 1), int2bytes(j % 2 ^ (i * 8))).rest
Proof step 7:
j < ~(2 ^ (i * 8 - 1)) ∧ 0 < i ∧ j % 2 ^ (i * 8) = 0, j % 2 ^ (i * 8) = 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i + 1), int2bytes(j % 2 ^ (i * 8))).rest = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8)) + fix(i→n(i) + 1, i2b(0) ').rest

Rule argument

name: int2bytes-rec-neg-04 rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: ⊦ i < ~ j ↔ i + j < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j, i