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Theorem refs-equal

⊦ # st .refs = # st0 .refs ∧ st ⊆ st0 ∧ r ∈ st0 → r ∈ st

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: 13
Proof steps: 28
Used lemmas: instore-inrefs-02, refs-def, refs-del, refs-empty, refs-empty-01,
Used spec theorems:
- set-basic/references/sel
- set-union/references/del-size
- store/javastore/Subset
- storefuns/delete-at
- storefuns/refin-del
Used simplifier rules:
- storefuns/delete-at
- storefuns/in-del
- refkey/elim
- storefuns/subset-notin
- storefuns/del-notin-01
- set-union/references/del-in
- set-union/references/del-size
- nat/lels
- nat/leprf
- set-basic/references/ne-01
- set-basic/references/Size-empty
- store/javastore/subset-empty
- storefuns/in-empty
- set-basic/references/size-zero-02