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Proof step 7 from proof exinpot (previous step)

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

User applied rule exists right

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

Rule argument

pos: right 1 terms: i0 abort: F discard: F computed: F

Additional information

Used terms: i0