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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ ¬ i < i; (s)% ⊦ i +1 = i + 1; (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ 1 ≤ i ↔ 0 < i; (s)%numlsf-02: ⊦ (* i) < j → i + 1 ≤ j; (forward) from specification int-abs