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Theorem pos-equal

⊦ a ∈ x ∧ pos(a, x) = n → (pos(b, x) = n ↔ a = b)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: possize-notin,
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: pos-y, pos-n, pos-e,
Used spec theorems:
- Used simplifier rules:
  - list/in-empty
  - list/in-rec
  - list/c
  - list/a
  - nat-basic2/z-01
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/eq-01