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Theorem get-firstn

⊦ n < m ∧ m ≤ # x → firstn(m, x)[n] = x[n]

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 11
Used lemmas: get-succ, get-zero-01, firstN-rec, get-rec, one-03, firstn-one-02,
Used spec theorems:
- Used simplifier rules:
  - nat/le-ls-simp
  - list/len-05
  - list/app
  - list-data/size-01
  - nat/lez-01
  - nat/one-02
  - nat-basic1/lf-02
  - nat-basic1/lf-01
  - nat/let
  - nat/lels
  - nat-basic2/s
  - nat/lep-02
  - list/e-01
  - list/c
  - list/c-08
  - list/c-07
  - nat-basic2/succ
  - nat/elim-pred-c
  - list-data/l
  - nat/fle
  - nat-basic1/f
  - nat/succ-01
  - list/a
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/oz