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Theorem keys-in-elim-last-oc

⊦ key ∈ keys(fs, ax) ↔ (∃ ax0, ax1, adr. ax = ax0 + adr ' + ax1 ∧ fs[adr].key = key ∧ ¬ key ∈ keys(fs, ax1))

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: 4
Proof steps: 10
Used lemmas: keys-base, keys-rec, keys-append,
Used spec theorems:
- Used simplifier rules:
  - list/key-list-set/in-10
  - list/key-list-set/in-append
  - list/key-list-set/in-empty
  - list/key-list-set/a
  - list/key-list-set/in-rec
  - list/key-list-set/c
  - list/address-list-set/c
  - list/address-list-set/Nil
  - list/address-list-set/a
  - list/address-list-set/app-08