Mathlib Map

Theorems · Theorem · order theory

map_inv_le_map_inv_iff

∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] [inst_2 : EquivLike F α β]
  [OrderIsoClass F α β] (f : F) {a b : β}, EquivLike.inv f b ≤ EquivLike.inv f a ↔ b ≤ a
Defined in
Mathlib.Order.Hom.Basic
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
LELEEquivLikeOrderIsoClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsPredArchimedean.of_orderIso · cited by 0IsPredArchimedean.of_orde…IsSuccArchimedean.of_orderIso · cited by 0IsSuccArchimedean.of_orde…EquivLike · cited by 165EquivLikeEquivLike.inv · cited by 42EquivLike.invOrderIsoClass · cited by 15OrderIsoClassEquivLike.apply_inv_apply · cited by 11EquivLike.apply_inv_applymap_inv_le_map_inv_iffCITED BYCITES

Cites4

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

Cited by2

Results whose statement or proof uses this declaration.