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Theorem ext

⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)

Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by: add-inter-rem, add-rem-sub, del-addeq-06, delete-shift, delsw-suc, diff-del-minus, diff-del-minus-2, diff-del-minus-3, diff-del-plus-1, diff-del-plus-2, diff-supset-empty, empty-intersection-diff, equal-add-in, int-empty-one, inter-empty-diff, intersect-add-rem, intersect-empty-rem, intersection-insert, intersection-shift, k-delete-rec, k-diff-rec1, k-diff-rec2, k-intersect-base, k-intersect-rec1, k-intersect-rec2, k-union-base, k-union-rec1, k-union-rec2, rem-inter-empty3, rem-union-ins, sub-rem-inter-rem, subset-is-union, subseteq-inter-empty-empty, subseteq-rem-del, union-diff-union-same, union-inter-inter-union, union-rem-add, union-rem-unchdg, union-sub-rem-inter-empty, unsubdel,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 8
Used lemmas:
Used spec theorems:
- infset-union/ext
Used simplifier rules:
- infset-basic/ne-01