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Theorem sublist-lenrec-01

⊦ n < # x → sublist(0, n + 1, x) = sublist(0, n, x) + x[n]

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 8
Used lemmas: get-succ, firstN-rec, get-zero-01, firstN-zero, restN-zero, sublist-def, sub-zerorec-01,
Used spec theorems:
- Used simplifier rules:
  - list/Last
  - nat/ls-le-simp
  - list-data/elim-list-c
  - nat/lels
  - nat-basic2/s
  - list/len-05
  - list/e-01
  - list/app
  - list/Nil
  - list/c-04
  - list-data/l
  - nat-basic1/f
  - nat/succ-01
  - list/app-08
  - list/c-08
  - list/c-07
  - list/a
  - nat-basic2/c
  - nat-basic2/a
  - list/c
  - nat-basic2/succ