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Theorem subset-is-union

⊦ st ⊆ st1 ↔ (∃ st0. st1 = st0 ∪ st ∧ st .keys ∩ st0 .keys = ∅)

Type: A user defined theorem
Validity: The proof is valid.
Features:
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: 50
Used lemmas: union-at-right-01, lookup-xtra, union-at-left, union-in, union-rec, union-empty, union-subset,
Used spec theorems:
- store/javastore/subset-put-02
- ostore/javastore/del-01
- store/javastore/ins
- ostore/javastore/Keys
- store/javastore/Extension
- set-union/javastore/ext
- store/javastore/Subset
Used simplifier rules:
- set-union/javastore/Intersect
- set-union/javastore/Delete
- set-basic/javastore/In-insert
- set-union/javastore/int-empty-02
- set-basic/javastore/In-empty
- set-basic/javastore/size-zero
- set-basic/javastore/size-zero-01
- set-union/javastore/intdel-empty
- store/javastore/Del-at
- store/javastore/notmemlookup
- javastore/lookup-if
- store/javastore/Del-in
- store/javastore/In-insert
- ostore/javastore/notempty
- set-basic/javastore/ne-01
- store/javastore/insins
- set-union/javastore/int-ins
- store/javastore/del-notin
- store/javastore/In-store
- ostore/javastore/insert-03
- store/javastore/subset-empty
- ostore/javastore/empty
- set-union/javastore/int-e
- set-union/javastore/int-a
- set-union/javastore/int-c