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Proof step 25 from proof prime-def-prime (previous step)

0 < i1, 1 < i1, 1 < i0 * i1, i0 < i1, 1 < i0, 0 < i0, j * j < i1, prime(j), j | i0, i0 ≤ i1, j * j ≤ i0, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦ prime(i0)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: j

Additional information

Used simplifier rules: divides-mult-01: ⊦ i | j → i | j * j0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≤ j ↔ ¬ j < i; (ss)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ 0 < i → (i * j < i ↔ j < 1); (s)% ⊦ i < 1 ↔ i ≤ 0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: j