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Proof step 13 from proof all_prime_divisors-rec-02 (previous step)

prime(i), 0 < j, 0 < i, i * j < 2 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic1 inst: name: two-ls seq: ⊦ 0 < j → (j < 2 ↔ j = 1) subst: [j] → [i * j] flags: rewrite

Additional information

Used simplifier rules: eq-one: ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = 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%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i * j