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Proof step 100 from proof isSquare-mult-aux (previous step)

max_prime_divisor(j0) * i0 = j0, i0 * i0 = i * i * i2, prime(max_prime_divisor(j0)), 0 < i, 0 < j0, 0 < max_prime_divisor(j0) * max_prime_divisor(j0) * i2, isSquare(i2), ∀ j1, j, i. i→n(j1) < i→n(j0) → j1 * j1 = j * i * i ∧ 0 < j1 ∧ 0 < j ∧ 0 < i → i = 0 ∨ isSquare(j) ⊦ i = 0, max_prime_divisor(j0) = 0, max_prime_divisor(j0) | i, isSquare(max_prime_divisor(j0) * max_prime_divisor(j0) * i2), prime(j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-square inst: name: isSquare-def seq: ⊦ isSquare(i) ↔ (∃ j. j * j = i) subst: [i] → [i2] flags: rewrite

Additional information

Used simplifier rules: square-eq: ⊦ i * i = j * j ↔ abs(i) = abs(j); from specification int-mult%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult%abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%isSquare-square: ⊦ isSquare(i * i); from specification int-square Used terms: i2