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Theorem to-plus-from-fin

⊦ n ≤ # x → (x to n) + (x from n) = x

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: elim-fromto, elim-fromto-fin,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 6
Used lemmas: from-succ-cons-l-lem, to-succ-cons-l-lem, from-zero-l, to-zero-l,
Used spec theorems:
- Used simplifier rules:
  - list-data/size-01
  - nat/lez-01
  - list/len-05
  - list/Nil
  - nat/lep-02
  - list/app-08
  - list/a
  - nat-basic2/c
  - nat-basic2/a
  - list/c
  - nat-basic2/succ