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Proof step 44 from proof equal-minus-one (previous step)

i ^ ~ j = ~1, j < 0 ⊦ i = ~1, i = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 46:
i ^ (~ j)-1 * i = ~1, j < 0, 0 < ~ j ⊦ i = 0, i = ~1, j = 0

Rule argument

spec: <toplevel> name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [~ j, i] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < j → ¬ j < i; (s) Used terms: ~ j, i