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Proof step 6 from proof notneg (previous step)

i ^ j < j, i ^ j < i, i ^ j < 0, 0 ≤ j, 0 ≤ i, i ^ j ≤ 1 ⊦ 1 < i ∧ 0 < j

User applied rule case distinction

And obtained the following new goals

Proof step 7:
i ^ j < 0, i ^ j < i, i ^ j < j, i ^ j ≤ 1, 0 ≤ i, 0 ≤ j ⊦ 1 < i

Rule argument

pos: right 1

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs