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Proof step 12 from proof pot-isSquare (previous step)

0 < i, isSquare(i ^ (j - 2) * i * i), 1 < j, 0 < j, ∀ 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 apply induction

And obtained the following new goals

Rule argument

subst: [j0, i] → [j - 2, i]

Additional information

Used simplifier rules: isSquare-mult: ⊦ isSquare(j * i * i) ↔ isSquare(j) ∨ i = 0;%even-not: ⊦ ¬ even(i) → ¬ even(i - 2); from specification int-min%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%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%num-between: i + 1 = i0 ⊦ (* i) < j → (j ≤ (* i0) ↔ j = i0); 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%isSquare-square: ⊦ isSquare(i * i); from specification int-square%isSquare-one: ⊦ isSquare(1); from specification int-square%even-2: ⊦ even(2); from specification int-min Used terms: j - 2, i