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Proof step 9 from proof intshiftrsign-2pot-neg (previous step)

i % 2 ^ j = 0, 0 < j, i < 0, j < 32, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ i % 2 ^ j0 = 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = i / 2 ^ j0 ⊦ ((i - 1) / 2) % 2 ^ (j - 1) = 0 ∧ j ≠ 1, (i - 1) / 2 i>> (j - 1) = i / 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 11:
2 ^ j ≠ 0, ∃ j0. i = j0 * 2 ^ j, 0 < j, i < 0, j < 32, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ i % 2 ^ j0 = 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = i / 2 ^ j0 ⊦ ((i - 1) / 2) % 2 ^ (j - 1) = 0 ∧ j ≠ 1, (i - 1) / 2 i>> (j - 1) = i / 2 ^ j

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [2 ^ j, i] rotate: F spec: int-div inst: name: modex

Additional information

Used simplifier rules: ⊦ 0 < j → (i ^ j = 0 ↔ i = 0); Used terms: 2 ^ j, i