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Theorem alldisjointp-reduce

⊦ alldisjointp(ts, f) → ( alldisjointp(ts, f0) ↔ (∀ tid1, tid2, np. (tid1 ∈ ts ∧ tid2 ∈ ts ∧ tid1 ≠ tid2 ∧ np ∈ f(tid1) → ¬ np ∈ f(tid2)) → tid1 ∈ ts ∧ tid2 ∈ ts ∧ tid1 ≠ tid2 ∧ np ∈ f0(tid1) → ¬ np ∈ f0(tid2)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state: VF3conc, VF3conc,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 9
Used lemmas: alldisjointp-def,
Used spec theorems:
- Used simplifier rules:
  - set-basic/tidset-npset/size-zero-01
  - set-basic/tidset-npset/ne-01