-- Module: Mathlib.ModelTheory.Algebra.Ring.FreeCommRing
Goal:
α : Type u_1
R : Type u_2
inst : CommRing R
inst_1 : CompatibleRing R
p : FreeCommRing α
v : α → R
l : ℕ
f : ring.Functions l
a : Fin l → ring.Term α
ih :
  ∀ (a_1 : Fin l),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (a a_1))
func :
  ∀ (a : Fin 2 → ring.Term α)
    (ih :
      ∀ (a_1 : Fin 2),
        Term.realize (L := ring) v (sorry p) =
          (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
              (a : FreeCommRing α) → R)
            (Term.realize FreeCommRing.of (a a_1))),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (Language.func ringFunc.add a))
func₁ :
  ∀ (a : Fin 2 → ring.Term α)
    (ih :
      ∀ (a_1 : Fin 2),
        Term.realize (L := ring) v (sorry p) =
          (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
              (a : FreeCommRing α) → R)
            (Term.realize FreeCommRing.of (a a_1))),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (Language.func ringFunc.mul a))
func₂ :
  ∀ (a : Fin 1 → ring.Term α)
    (ih :
      ∀ (a_1 : Fin 1),
        Term.realize (L := ring) v (sorry p) =
          (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
              (a : FreeCommRing α) → R)
            (Term.realize FreeCommRing.of (a a_1))),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (Language.func ringFunc.neg a))
func₃ :
  ∀ (a : Fin 0 → ring.Term α)
    (ih :
      ∀ (a_1 : Fin 0),
        Term.realize (L := ring) v (sorry p) =
          (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
              (a : FreeCommRing α) → R)
            (Term.realize FreeCommRing.of (a a_1))),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (Language.func ringFunc.zero a))
func₄ :
  ∀ (a : Fin 0 → ring.Term α)
    (ih :
      ∀ (a_1 : Fin 0),
        Term.realize (L := ring) v (sorry p) =
          (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
              (a : FreeCommRing α) → R)
            (Term.realize FreeCommRing.of (a a_1))),
    Term.realize (L := ring) v (sorry p) =
      (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
          (a : FreeCommRing α) → R)
        (Term.realize FreeCommRing.of (Language.func ringFunc.one a))
⊢ Term.realize (L := ring) v (sorry p) =
    (((FreeCommRing.lift : (a : α → R) → FreeCommRing α →+* R) v : RingHom.{u_1, u_2} (FreeCommRing α) R) :
        (a : FreeCommRing α) → R)
      (Term.realize FreeCommRing.of (Language.func f a))

Tactic:
cases f