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Theorem first-num

n ≠ 0 ⊦ firstn((* n), x) = x.first ' + firstn(n -1, x.rest)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: firstn-one-01, firstn-one-02, sublist-append-04, sublist-move, sublist-not-empty-02, sublist-one, sublist-part, sublist-prefix,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 3
Used lemmas: firstN-rec,
Used spec theorems:
- Used simplifier rules:
  - nat/pred-03
  - nat-basic2/oz
  - nat-basic2/a
  - nat-basic2/c
  - list/c
  - list/app-08
  - list/a
  - nat/elim-pred-c