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Proof step 30 from proof prime-def-prime (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); (s)%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; (s)% ⊦ 0 < i → (i < i * j ↔ 1 < j); (s)% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult