Mathlib Map

Theorems · Theorem · order theory

OrderIso.isSimpleOrder

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : BoundedOrder α]
  [inst_3 : BoundedOrder β] [h : IsSimpleOrder β] (f : α ≃o β), IsSimpleOrder α
Defined in
Mathlib.Order.Atoms
Cited by
3 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPartialOrderBoundedOrderBoundedOrderIsSimpleOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsSimpleModule.congr · cited by 15IsSimpleModule.congrIsSimpleRing.of_surjective · cited by 0IsSimpleRing.of_surjectiveIsSimpleRing.of_ringEquiv · cited by 0IsSimpleRing.of_ringEquivPartialOrder · cited by 6410PartialOrderOrderIso · cited by 874OrderIsoBoundedOrder · cited by 270BoundedOrderIsSimpleOrder · cited by 54IsSimpleOrderOrderIso.isSimpleOrder_iff · cited by 12OrderIso.isSimpleOrder_iffOrderIso.isSimpleOrderCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.