Mathlib Map

Theorems · Definition · order theory

IsSimpleOrder.equivBool

{α : Type u_4} → [DecidableEq α] → [inst : LE α] → [inst_1 : BoundedOrder α] → [IsSimpleOrder α] → α ≃ Bool

Every simple lattice is isomorphic to Bool, regardless of order.

Defined in
Mathlib.Order.Atoms
Cited by
4 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
DecidableEqLEBoundedOrderIsSimpleOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Fintype.IsSimpleOrder.card · cited by 0IsSimpleOrder.cardIsSimpleOrder.equivBool.congr_simp · cited by 0equivBool.congr_simpIsSimpleOrder.equivBool_apply · cited by 0IsSimpleOrder.equivBool_a…IsSimpleOrder.equivBool_symm_apply · cited by 0IsSimpleOrder.equivBool_s…IsSimpleOrder.orderIsoBool · cited by 0IsSimpleOrder.orderIsoBoolTop.top · cited by 9680Top.topEquiv · cited by 8337EquivBot.bot · cited by 4720Bot.botBoundedOrder · cited by 270BoundedOrderIsSimpleOrder · cited by 54IsSimpleOrderIsSimpleOrder.equivBoolCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.