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Theorem disjoint-all

⊦ disjoint(s, s0) ↔ (∀ a. ¬ a ∈ s ∨ ¬ a ∈ s0)

Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by: disjoint-01, disjoint-diff, disjoint-diff-subset, disjoint-diff1, disjoint-diff2, disjoint-empty, disjoint-empty2, disjoint-notempty-01, disjoint-rec, disjoint-rec2, disjoint-rem, disjoint-sym, disjointu-empty, disjointu-empty2, int-inse, int-inserte, rem-disjoint, subset-disjoint-union, subseteq-disjoint-empty,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: int-c, int-a, Intersect, Disjoint,
Used spec theorems:
- set-basic/Extension
Used simplifier rules: