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Proof step 8 from proof square-neq-prime (previous step)

j * j = i * j0 * j0, j0 < 0, 0 < j, prime(i) ⊦ j = 0

User applied rule apply lemma

And obtained the following new goals

Proof step 9:
⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 → j * j ≠ i * j0 * j0

Rule argument

spec: <toplevel> name: square-neq-pos seq: ⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 → j * j ≠ i * j0 * j0 subst: [i, j, j0] → [i, j, ~ j0]

Additional information

Used simplifier rules: ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~ i * j = ~(i * j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ ~ ~ i = i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: i, j, ~ j0