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Theorem keyset-subarray-eq-add

m ≤ # kar0, m ≤ # kar1 ⊦ subarray(kar0, 0, m) = subarray(kar1, 0, m) ∧ ¬ ki0 ∈ keyset(kar0, m) → (keyset(kar0, m) ++ ki0 = keyset(kar1, m) ++ ki1 ↔ ki0 = ki1)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas: keyset-subarray-eq,
Used spec theorems:
- Used simplifier rules:
  - nat/lels-02
  - set-basic/keyindex-set/in-05
  - set-basic/keyindex-set/eq
  - nat-basic/f
  - array-copy/key-index-array/subarray-elim