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Proof step 38 from proof le-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [i1, i0] flags: <all paths>

Additional information

Used simplifier rules: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; (s)% ⊦ i + 1 ≤ j ↔ i < j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: i1, i0