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Proof step 37 from proof le-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%succ-01: ⊦ i + 1 ≤ j ↔ i < j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: i1, i0