{α : Type u_8} →
  {motive : CompleteSemilatticeInf α → Sort u} →
    ([toPartialOrder : PartialOrder α] →
        [toInfSet : InfSet α] →
          (sInf_le : ∀ (s : Set α), ∀ a ∈ s, sInf s ≤ a) →
            (le_sInf : ∀ (s : Set α) (a : α), (∀ b ∈ s, a ≤ b) → a ≤ sInf s) →
              motive
                { toPartialOrder := toPartialOrder, toInfSet := toInfSet, sInf_le := sInf_le, le_sInf := le_sInf }) →
      (t : CompleteSemilatticeInf α) → motive t