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Theorem insub-01

⊦ a ∈ y ∧ x ∪ y ⊆ z → a ∈ z

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas: sub-notin, rmdup, assoc, union,
Used spec theorems:
- Used simplifier rules:
  - list/a
  - list/in-12