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Proof step 13 from proof prime-def-prime (previous step)

0 < i, 1 < 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) ⊦ 2 ≤ i ∧ (∀ i0. 1 < i0 ∧ i0 < i → ¬ i0 | i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs