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Theorem notmemlookup

⊦ ¬ a ∈ st → st[a] = (∅)[a]

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: At-in-out, Del-other-data, empty-01, eq-shift-del, eq-shift-put, exnotempty, ext-rec, indef-01, inj-put, inj-put-01, ins-same, k-Extension, lookupisempty, neq, notin-del-notin, subset-empty-01, sw-01,
Used by units in proved state: path-reachable, ostore, store+set,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: At-other, In-insert, gen-04,
Used spec theorems:
- Used simplifier rules: