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Proof step 2 from proof intshiftrsign-2pot-neg-02 (previous step)

j < 32, i < 0, 0 < j ⊦ i % 2 ^ j = 0, i / 2 ^ j = (i i>> j) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j
Proof step 4:
i < 0 ∧ 0 < j ∧ j < 32, j < 32, i < 0, 0 < j ⊦ i % 2 ^ j = 0, i / 2 ^ j = (i - (2 ^ j - 1)) / 2 ^ j + 1

Rule argument

name: intshiftrsign-2pot-neg-01 rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: j, i