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Theorem elim-lastn-butlastn

⊦ n ≤ # x → (y = butlastn(n, x) ∧ z = lastn(n, x) ↔ x = y + z ∧ # z = n)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: lastN-in-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: restN-len, lastn-restn-01, firstN-len, blastN-firstN, lastn-length-01, lastN-blastN,
Used spec theorems:
- Used simplifier rules:
  - nat/lep
  - list/len
  - list/a
  - nat/eq-01
  - nat-basic2/a
  - nat-basic2/c
  - nat/lels-01
  - nat-basic2/l-02