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Theorem prefix-at

⊦ adr ∈ st0 ∧ st0 ⊑ st1 → st0[adr] = st1[adr]

Type: A user defined theorem
Validity: The proof is valid.
Features: forward, localforward,
Comment:
Used by:
Used by units in proved state: ablock-nodes,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 12
Proof steps: 30
Used lemmas: in, blockstore-prefix, at,
Used spec theorems:
- set-union/nat-set/subdef
- list/laddress-list/firstoc-rew
- list-last/laddress-list/prefix
- list-last/prefix
- list-del/get-append-less
Used simplifier rules:
- address-data/elim
- ablock/elim
- store+set/ablock-store-nat-store/Dom
- list-last/laddress-list/prefix-in-01
- ablock/sel-02
- ablock/sel-01
- address-data/sel-05
- address-data/sel-04
- address-data/sel-03
- list/laddress-list/in-rec
- list/laddress-list/in-append
- nat-basic/add-base
- list-del/laddress-list/pos-y
- list-del/laddress-list/app-05-neg
- nat-basic/succ
- list/laddress-list/a
- list/laddress-list/len-05
- list/laddress-list/len
- list/len
- nat/lels
- list/a
- list-del/get-append-grt
- nat/elim-sub
- nat-basic/eq-01
- nat-basic/a
- nat-basic/c
- nat-basic/eq-02
- nat-basic/z-01
- nat-basic/oz