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Proof step 6 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 i>> (j - 1) = i / 2 ^ j

User applied rule apply induction

And obtained the following new goals

Proof step 7:
(i - 1) / 2 < 0 ∧ ((i - 1) / 2) % 2 ^ (j - 1) = 0 ∧ 0 < j - 1 ∧ j - 1 < 32 → (i - 1) / 2 i>> (j - 1) = ((i - 1) / 2) / 2 ^ (j - 1), 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 i>> (j - 1) = i / 2 ^ j

Rule argument

subst: [i, j0] → [(i - 1) / 2, j - 1]

Additional information

Used simplifier rules: ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: (i - 1) / 2, j - 1