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Theorem del-rax

⊦ a ∈ s -- b ↔ ¬ ¬(a ≠ b ∧ a ∈ s)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-inter-rem, del-addeq, del-addeq-01, del-addeq-05, del-addeq-06, del-addin-01, del-d, del-d-01, del-e-02, del-eq, del-feq, del-feq-02, del-in, del-in-01, del-neq-01, del-three, del-two, delete-shift, delsw, delsw-02, diff-add-del, diff-del-02, diff-del-minus, diff-del-minus-2, diff-del-minus-3, diff-subset-01, equal-add-in, int-del-rew, intersect-add-rem, k-delete-rec, k-diff-rec1, k-intersect-rec1, k-intersect-rec2, sub-ade, sub-ade-01, sub-ade-02, sub-ade-03, sub-del, sub-del-02, sub-del-04, sub-del-05, subseteq-rem-del, subsub-del, undel, undel-01, undel-04, undel-06, unindel, uninsubdel, union-del, unsubdel,
Used by units in proved state: ostore, oset, store+set,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas: Delete,
Used spec theorems:
- Used simplifier rules: