∀ {α : Type u_1} [inst : CompleteLattice α] {s : α} [inst_1 : SizeOf α] (parts : Set α) (sSupIndep' : sSupIndep parts)
  (bot_notMem' : ⊥ ∉ parts) (sSup_eq' : sSup parts = s),
  sizeOf { parts := parts, sSupIndep' := sSupIndep', bot_notMem' := bot_notMem', sSup_eq' := sSup_eq' } =
    1 + sizeOf sSup_eq'