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Proof step 11 from proof le-pos-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: pnle-pos seq: i ≤ i0, j < j0, i0 ≠ 0, 0 ≤ i, 0 ≤ j ⊦ ¬ i0 * j0 ≤ i * j subst: [j, i, j0, i0] → [i0, i0 ^ i1, i, i ^ i1] flags: rewrite

Additional information

Used simplifier rules: pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i);%notneg: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i ^ j < 0;%Pot-zero: ⊦ j ^ 0 = 1;%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs Used terms: i0, i0 ^ i1, i, i ^ i1