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Proof step 55 from proof equal-minus-one (previous step)

~1 = j % 2, j < 0 ⊦ 1 / ~1 ^ ~ j = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ 0 < j ∧ j % 2 = 1 → ~1 ^ j = ~1

Rule argument

spec: <toplevel> name: minus-one-odd seq: ⊦ 0 < j ∧ j % 2 = 1 → ~1 ^ j = ~1 subst: [j] → [~ j] flags: <all paths>

Additional information

Used simplifier rules: j ≠ 0 ⊦ ~ i % j = ~(i % j); (s)% ⊦ ~ i = j ↔ i + j = 0; (s)% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < ~ i ↔ i < 0; (s) Used terms: ~ j