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Proof step 43 from proof equal-minus-one (previous step)

~((1 - ~(i ^ ~ j)) / ~(i ^ ~ j) + 1) = ~1, i ^ ~ j < 0, j < 0, 0 < ~(i ^ ~ j), ~(i ^ ~ j) ≤ 1 ⊦ i = ~1, i = 0, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
i ^ ~ j = ~1, j < 0 ⊦ i = ~1, i = 0, j = 0

Rule argument

Additional information

Used simplifier rules: zero-02: ⊦ j < 0 → (i ^ ~ j = 0 ↔ i = 0);%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); (s)% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)% ⊦ ~ i ≤ j ↔ 0 ≤ i + j; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ ~(i - j) = j - i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + ~ j = i - j; (s)%j ≠ 0 ⊦ i / ~ j = ~(i / j); (s)% ⊦ i - ~ j = i + j; (s)