Theorems · Theorem · order theory

Quotient.mk_le_mk

∀ {α : Type u_1} {s : Setoid α} [inst : LinearOrder α] [H : ∀ (x : Quotient s), (Quotient.mk s ⁻¹' {x}).OrdConnected]
  {x y : α}, ⟦x⟧ ≤ ⟦y⟧ ↔ x ≤ y ∨ x ≈ y

Defined in

Mathlib.Order.Quotient

Cited by

2 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderSet.OrdConnected