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Proof step 33 from proof le-pos (previous step)

~1 ≤ i0, 0 ≤ i0, ~2 < i0, 1 < i, 2 ≤ i, 0 ≤ i1, ∀ j1, i, j0. i→n(j1) < i→n(i0 +1) → 2 ≤ i ∧ 0 ≤ j1 ∧ 1 < i → (i ^ j1 ≤ i ^ j0 ↔ j1 ≤ j0) ⊦ i ^ i0 * i ≤ i ^ i1 * i ↔ i0 < i1 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: le-pos-01 seq: ⊦ 0 < i → (j * i ≤ i0 * i ↔ j ≤ i0) subst: [i0, i, j] → [i ^ i1, i, i ^ i0] flags: rewrite

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: i ^ i1, i, i ^ i0