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Proof step 56 from proof rightshift-8-01-01 (previous step)

⊦ ~(2 ^ (8 * abs(j))) % 2 ^ (8 * abs(j)) = 0, j = 0, ~(2 ^ (8 * abs(j))) / 2 ^ (8 * abs(j)) = 0, int2bytes(~(2 ^ (8 * abs(j)))).first = i2b(~1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
j ≠ 0 ⊦ ~ i % j = ~(i % j)
Proof step 58:
¬ 2 ^ (8 * abs(j)) ≠ 0 ⊦ ~(2 ^ (8 * abs(j))) % 2 ^ (8 * abs(j)) = 0, j = 0, ~(2 ^ (8 * abs(j))) / 2 ^ (8 * abs(j)) = 0, int2bytes(~(2 ^ (8 * abs(j)))).first = i2b(~1)

Rule argument

seq: j ≠ 0 ⊦ ~ i % j = ~(i % j) subst: [j, i] → [2 ^ (8 * abs(j)), 2 ^ (8 * abs(j))] rotate: F spec: int-div inst: name: mod-neg-01

Additional information

Used simplifier rules: ⊦ i * j = j * i;%i ≠ 0 ⊦ i % i = 0; Used terms: 2 ^ (8 * abs(j)), 2 ^ (8 * abs(j))