(* Note: this is Tait's iii, or Girard's CR4 *)
definition S2 ≝ λRR:lenv→relation term. λRS:relation term. λRP,C:lenv→predicate term.
∀L,Vs. all … (RP L) Vs →
- ∀T. 𝐒[T] → NF … (RR L) RS T → C L (ⒶVs.T).
+ ∀T. 𝐒⦃T⦄ → NF … (RR L) RS T → C L (ⒶVs.T).
(* Note: this is Tait's ii *)
definition S3 ≝ λRP,C:lenv→predicate term.