Mathlib Map

Theorems · Theorem · order theory

inf_le_iff

∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, min b c ≤ a ↔ b ≤ a ∨ c ≤ a
Defined in
Mathlib.Order.Lattice
Cited by
6 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

min_le_iff · cited by 15min_le_iffFinset.inf_le_iff · cited by 2Finset.inf_le_iffArchimedeanClass.min_le_mk_sub · cited by 1ArchimedeanClass.min_le_m…List.minimum_le_coe_iff · cited by 0List.minimum_le_coe_iffmin_le_of_add_le_two_nsmul · cited by 0min_le_of_add_le_two_nsmulAlgebraicGeometry.Scheme.ord_add · cited by 0Scheme.ord_addLinearOrder · cited by 8572LinearOrderinf_le_iffCITED BYCITES

Cites1

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

Cited by6

Results whose statement or proof uses this declaration.