∀ {ι : Type u_1} {α : ι → Type u_2} [inst : LinearOrder ι] [inst_1 : (i : ι) → CompleteLinearOrder (α i)]
  [inst_2 : WellFoundedLT ι] (a b c : Lex ((i : ι) → α i)), a ≤ b → a ≤ c → a ≤ Lattice.inf b c