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Theorem disj-in-both

n0 < m, n1 < m ⊦ disj(asar, 0, m) ∧ adr ∈ asar[n0] → (adr ∈ asar[n1] ↔ n0 = n1)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: disj-union-rem, disj-unique, union-write,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 5
Used lemmas: disj,
Used spec theorems:
- Used simplifier rules:
  - set-basic/address-list-set/size-zero-01
  - nat-basic/f
  - set-basic/address-list-set/ne-01
  - nat-basic/c
  - nat-basic/a
  - nat-basic/add-base
  - set-union/address-list-set/int-a
  - set-union/address-list-set/int-c
  - set-union/address-list-set/int-empty-02