∀ {L : FirstOrder.Language} {M : Type u_1} [inst : L.Structure M] {L' : FirstOrder.Language} [inst_1 : L'.Structure M]
  (φ : L →ᴸ L') [inst_2 : φ.IsExpansionOn M] (S T : L'.Substructure M),
  (fun S => { carrier := ↑S, fun_mem := ⋯ }) S = (fun S => { carrier := ↑S, fun_mem := ⋯ }) T → S = T