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Theorem keys-same-fs

⊦ fs0 | ax1.toSet = fs1 | ax1.toSet → keys(fs0, ax1) = keys(fs1, ax1)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 22
Proof steps: 41
Used lemmas:
Used spec theorems:
- list/key-list-set/firsteq
- store/node-store/Extension
- store+set/node-store/restrict-in
- store/node-store/notmemlookup
- store+set/node-store/restrict-at
Used simplifier rules:
- list+set/address-list-set/toSet-empty
- store+set/node-store/restrict-empty
- aubifs-base/keys-base
- list/key-list-set/c
- aubifs-base/keys-rec
- list/address-list-set/a
- set-union/node-store/unc
- set-union/node-store/una
- set-union/node-store/une
- set-union/node-store/unadd
- list+set/address-list-set/toSet-one
- list+set/address-list-set/toSet-app
- list/address-list-set/c
- list/key-list-set/a
- list/key-list-set/Nil
- list/key-list-set/rest
- list/key-list-set/first
- list/key-list-set/e
- store/node-store/notmemlookup
- store+set/node-store/restrict-in
- list+set/address-list-set/toSet-ext
- set-basic/node-store/In-insert
- store+set/node-store/restrict-at