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Proof step 2 from proof notneg-01 (previous step)

0 < i, i ^ j ≤ 0, 0 ≤ j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
0 < i, i ^ j < i, i ^ j ≤ 0, i ^ j ≤ j, 0 ≤ j ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ 1 ≤ i ↔ 0 < i; (s)%numlef-01: ⊦ (* i) ≤ j → i - 1 < j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%numlsf-02: ⊦ (* i) < j → i + 1 ≤ j; (forward) from specification int-abs