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Theorem subdef

⊦ s1 ⊆ s2 ↔ (∀ a. a ∈ s1 → a ∈ s2)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: delete-subset, diff-del-01, diff-del-02, diff-one, diff-sub, diff-subset, diff-subset-01, insdel-sub, int-eq, int-idem, int-subs01, selsub-diff, sub-ade, sub-ade-01, sub-ade-02, sub-ade-03, sub-del, sub-del-01, sub-del-02, sub-del-03, sub-del-04, sub-del-05, sub-union, sub-union-01, sub-union-02, sub-union-03, sub-union-04, sub-union-05, subset-del, subsub-del, uneq, unidem, union-difference, union-sub-01, unsub, unsub-union-01, unsubdel, unsubins, unsubins-01, unsubsub,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: ext,
Used spec theorems:
- infset-union/subdef
Used simplifier rules: