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Proof step 125 from proof int2bytes-rec-neg-05 (previous step)

int2bits(j % 2 ^ (i * 8)).rest = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 126:
⊦ int2bits(j).rest = [] ↔ j = 0 ∨ j = ~1
Proof step 127:
j % 2 ^ (i * 8) = 0 ∨ j % 2 ^ (i * 8) = ~1, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 ≤ i, j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 0 < i ⊦ j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest = []

Rule argument

seq: ⊦ int2bits(j).rest = [] ↔ j = 0 ∨ j = ~1 subst: [j] → [j % 2 ^ (i * 8)] rotate: F spec: int2bits inst: name: int2bits-rest

Additional information

Used terms: j % 2 ^ (i * 8)