apply Schema.lookup_nth
case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
  HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
    (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
    lookupType sch
      { fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst,
        snd := hasNthName { val := n, isLt := (_ : n < length sch) } }
no goals