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Proof step 9 from proof pot-isSquare (previous step)

0 < i, 0 < j, isSquare(i ^ (j - 1) * i), ∀ j0, i. i→n(j0) < i→n(j) → isSquare(i ^ j0) ∧ 0 < i ∧ 0 < j0 → isSquare(i) ∨ even(j0) ⊦ isSquare(i), even(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 11:
0 < j - 1, 0 < i, 0 < j, isSquare((i ^ (j - 1)-1 * i) * i), ∀ j0, i. i→n(j0) < i→n(j) → isSquare(i ^ j0) ∧ 0 < i ∧ 0 < j0 → isSquare(i) ∨ even(j0) ⊦ isSquare(i), even(j)

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j - 1, i] flags: rewrite

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j - 1, i