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Theorem replay-cons-strong-append

nd.key = key ⊦ ¬ adr ∈ fs ∧ log-cons(log, fs) ∧ node-cons(key, nd) ∧ ri-cons(ri, fs) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) → (replay-cons-strong(fs[adr, nd], ri[key, adr], ro, fi, fo, log + adr ') ↔ replay-one(adr, nd, ri ⊖ ro) = ri[nd.key, adr] ⊖ ro)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 13
Used lemmas: replay-log-write, replay-safe-write, replay-safe-one, replay-safe-split, replay-log-one, replay-split, replay, replay-cons-strong,
Used spec theorems:
- aubifs-base/notin-dels
- store+set/node-index/Data-in
Used simplifier rules:
- list/address-list-set/a
- store/node-store/At-same
- node-store/in-insert
- aubifs-inv/log-adr-in
- aubifs-inv/ri-cons-in