From mathcomp Require Import all_ssreflect.

Fixpoint twice (n: nat): nat :=
  if n is n'.+1 then (twice n').+2 else 0.

Lemma twiceDouble: forall n:nat,
  twice (2 * n) = twice n + twice n.
Proof.
  elim=> [|n IHn].
  - done.
  - rewrite !addSn.
    rewrite -/twice.
    rewrite mulnS.
    rewrite -IHn.
Abort.

Context (A B C: Prop).

Lemma HilbertS: (A -> B -> C) -> (A -> B) -> A -> C.
Proof.
  move=> Habc Hab.
  move: Habc.