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Proof step 40 from proof equal-minus-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
1 / i ^ ~ j = ~1, j < 0, i ^ ~ j < 0 ⊦ i ^ ~ j = ~1, i = 0, i = ~1, j = 0

Rule argument

Additional information

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