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Proof step 11 from proof int-simp-04 (previous step)

i0 + i1 < ~1, 0 < i0, i0 + i1 < 0, ∀ i. ¬ i + i1 < 0 ∨ ¬ 0 < i1 ∨ ¬ 0 < i ⊦ i1 < 0

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: i0

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ ¬ i < j → (j < i ↔ i ≠ j); (ss)% ⊦ 0 + i = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j → ¬ j < i; (s) Used terms: i0