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Theorem firstn-last-rec

⊦ n ≠ 0 ∧ n ≤ # x → firstn(n, x) = firstn(n -1, x) + x[n -1]

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: 1
Proof steps: 9
Used lemmas: get-rec-01, get-zero, firstN-zero, firstN-rec,
Used spec theorems:
- Used simplifier rules:
  - nat/pred-03
  - list/Last
  - nat-basic2/pred
  - list/app
  - list/Nil
  - list/c-04
  - nat/elim-pred-c
  - nat/succ-01
  - nat-basic2/oz
  - list/app-08
  - list-data/elim-list-c
  - list-data/l
  - nat-basic1/f
  - nat-basic2/l
  - nat/lels
  - list/e-01
  - list/c
  - list/len-05
  - nat-basic2/succ
  - list/a
  - nat-basic2/s
  - nat/le-ls-simp
  - nat-basic2/a
  - nat-basic2/c
  - list/c-08
  - list/c-07