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Theorem upper-bound-reduce

⊦ upper-bound(ar, i) → (upper-bound(ar0, i0) ↔ (∀ n, m. (n + m ≤ # ar → sum(ar, n, m) ≤ i) → n + m ≤ # ar0 → sum(ar0, n, m) ≤ i0))

Type: A user defined theorem
Validity: The proof is valid.
Features: lss, s,
Comment: A generated reduce lemma variant for lemma: upper-bound
Used by: max-sum-keep-current-max, max-sum-new-current-max, max-sum-next-less-zero,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 11
Used lemmas: upper-bound,
Used spec theorems:
- Used simplifier rules:
  - int-abs/le-def
  - int-abs/lels-03