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Proof step 15 from proof le-pos (previous step)

2 ≤ i, 1 < i, ~2 < i0, ~1 ≤ i0, 0 ≤ i0, ∀ j1, i, j0. i→n(j1) < i→n(i0 +1) → 2 ≤ i ∧ 0 ≤ j1 ∧ 1 < i → (i ^ j1 ≤ i ^ j0 ↔ j1 ≤ j0) ⊦ i ^ i0 ≤ 0 ↔ i0 + 1 ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 < i ∧ 0 ≤ j → ¬ i ^ j ≤ 0
Proof step 17:
0 < i ∧ 0 ≤ i0, 2 ≤ i, 1 < i, ~2 < i0, ~1 ≤ i0, 0 ≤ i0, ∀ j1, i, j0. i→n(j1) < i→n(i0 +1) → 2 ≤ i ∧ 0 ≤ j1 ∧ 1 < i → (i ^ j1 ≤ i ^ j0 ↔ j1 ≤ j0) ⊦ false ↔ i0 + 1 ≤ 0

Rule argument

spec: int-pot inst: name: notneg-01 seq: ⊦ 0 < i ∧ 0 ≤ j → ¬ i ^ j ≤ 0 subst: [j, i] → [i0, i] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs Used terms: i0, i