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Theorem put-app-left

⊦ n < # x → (x + y)[n, a] = x[n, a] + y

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 7
Used lemmas: put-succ, put-zero, put-rec-02,
Used spec theorems:
- Used simplifier rules:
  - list/Nil
  - list-data/size-01
  - nat-basic1/zero-01
  - nat/lels
  - nat-basic2/s
  - nat-basic2/succ
  - list/len-05
  - nat/pred-03
  - nat/elim-pred-c
  - list-data/l
  - nat-basic1/f
  - nat/succ-01
  - list/app-08
  - list/a
  - list/c
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/oz