Instances on pempty

This file collects facts about algebraic structures on the (universe-polymorphic) empty type, e.g. that it is a semigroup.

instance SemigroupPEmpty : Semigroup PEmpty.{u + 1}

Equations

• SemigroupPEmpty = { mul := fun (x x_1 : PEmpty.{?u.1 + 1}) => PEmpty.casesOn (fun (t : PEmpty.{?u.1 + 1}) => x = t → PEmpty.{?u.1 + 1}) x ⋯, mul_assoc := ⋯ }

instance AddSemigroupPEmpty : AddSemigroup PEmpty.{u + 1}

Equations

• AddSemigroupPEmpty = { add := fun (x x_1 : PEmpty.{?u.1 + 1}) => PEmpty.casesOn (fun (t : PEmpty.{?u.1 + 1}) => x = t → PEmpty.{?u.1 + 1}) x ⋯, add_assoc := ⋯ }