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Proof step 8 from proof notneg (previous step)

i ^ j < 0, 0 ≤ i, 0 ≤ j, i ≤ 1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < i → j ^ i = j ^ i -1 * j

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: Pot-zero: ⊦ j ^ 0 = 1;%one-01: ⊦ 1 ^ j = 1;% ⊦ i -1 = i - 1; (s)% ⊦ 0 ≤ i → (i * j < 0 ↔ j < 0 ∧ i ≠ 0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s) Used terms: j, i