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Theorem Diff-ext

⊦ a ∈ st \ s ↔ a ∈ st ∧ ¬ a ∈ s

Type: A user defined theorem
Validity: The proof is valid.
Features: cut, simp, localsimp,
Comment:
Used by: Diff-Diff-com, Diff-del-rw, Diff-mems-get, diff-add-notin, dom-rem, rem-write, rem-write-other, restrict-empty, restrict-in, restrict-intersect-empty,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 5
Used lemmas: Diff-rec, Diff-base,
Used spec theorems:
- store/Del-in
Used simplifier rules:
- set-basic/In-empty
- set-basic/rax