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Proof step 7 from proof exinpot (previous step)

1 < i, 0 < i, 0 < j, ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j - 1 ∧ j - 1 < i ^ (i0 + 1), ∀ j0, i. i→n(j0) < i→n(j) → 1 < i ∧ 0 < j0 → (∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j0 ∧ j0 < i ^ (i0 + 1)) ⊦ ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j ∧ j < i ^ i0 * i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
1 < i ^ i0 * i, 0 < i ^ i0, 0 < j, 1 < j, 1 < i, i ^ i0 < j, 0 < i, j ≤ i ^ i0 * i, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(j) → 1 < i ∧ 0 < j0 → (∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j0 ∧ j0 < i ^ (i0 + 1)) ⊦ ∃ i0. 0 ≤ i0 ∧ i ^ i0 ≤ j ∧ j < i ^ i0 * i

Rule argument

Additional information

Used simplifier rules: succ: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; (s)% ⊦ 0 < i → (i < i * j ↔ 1 < j); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 1 ≤ j ↔ i < j; (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)