English
A high-level induction principle for finite types: every finite type is equivalent to a base case built from Empty or Option α.
Русский
Высокий принцип индукции по конечным типам: любой конечный тип эквивалентен базовому случаю из Empty или Option α.
LaTeX
$$Finite.induction_empty_option$$
Lean4
/-- A finite bounded linear order is complete.
If the `α` is already a `BiheytingAlgebra`, then prefer to construct this instance manually using
`Fintype.toCompleteLattice` instead, to avoid creating a diamond with
`LinearOrder.toBiheytingAlgebra`. -/
noncomputable abbrev toCompleteLinearOrder [LinearOrder α] [BoundedOrder α] : CompleteLinearOrder α :=
{ toCompleteLattice α, ‹LinearOrder α›, LinearOrder.toBiheytingAlgebra _ with }
-- See note [reducible non-instances]
