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Theorem put-sw-in

⊦ m < # x ∧ n < # x → (a ∈ x[m, x[n]][n, x[m]] ↔ a ∈ x)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 16
Used lemmas: get-zero, put-in, get-in, put-succ, put-zero, get-rec,
Used spec theorems:
- Used simplifier rules:
  - list/in-empty
  - list-data/size-nil
  - nat-basic/less-zero
  - nat/lels
  - nat-basic/c
  - nat-basic/a
  - nat-basic/s-04
  - list/a
  - list/len-02
  - list/len
  - list/c
  - nat/lez
  - list/e
  - list/app-02
  - list/c-07
  - list/e-01
  - list/in-append
  - list/in-17
  - nat-basic/oz
  - nat/succ-01
  - nat/elim-pred-c
  - list-data/l
  - nat-basic/f