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Theorem at-write-at

⊦ # ax = # ndx ∧ adr ∈ ax ∧ ¬ dups(ax) → fs[ax, ndx][adr] = ndx[pos(adr, ax)]

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas: at-write-other, write-rec,
Used spec theorems:
- Used simplifier rules:
  - list-data/address-list-set/size-01
  - list-data/node-list/l
  - list-del/address-list-set/pos-e
  - list/address-list-set/in-empty
  - list-dup/address-list-set/dups-cons
  - list/address-list-set/in-rec
  - list/address-list-set/len-05
  - list/address-list-set/c
  - list-data/node-list/size-01
  - nat-basic/z-01
  - list-data/address-list-set/l
  - list-del/node-list/get-succ
  - list-del/address-list-set/pos-n
  - list-del/node-list/get-zero-01
  - list-del/address-list-set/pos-y
  - store/node-store/At-same
  - list/address-list-set/a
  - nat-basic/c
  - nat-basic/a
  - nat-basic/eq-01
  - list/node-list/a
  - nat-basic/succ
  - list/node-list/len-05
  - list/node-list/c