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Theorem in-get

⊦ a ∈ x ↔ (∃ n. n < # x ∧ x[n] = a)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: get-app, get-in,
Used spec theorems:
- list/In
Used simplifier rules:
- nat-basic2/s
- nat-basic2/succ
- list/len-05
- list/len
- list/c
- nat-basic2/l-02
- nat-basic2/a
- nat-basic2/c
- list/a