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Proof step 36 from proof le-pos (previous step)

i ^ i0 ≤ i ^ i1 ↔ i0 ≤ i1, 0 < i, ~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 ^ i1 ↔ i0 < i1 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
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) ⊦

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%irref: ⊦ ¬ i < i; from specification int-basic1%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%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%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%numlsf-02: ⊦ (* i) < j → i + 1 ≤ j; (forward) from specification int-abs