Theorems · Theorem · order theory

floorDiv_le_ceilDiv

∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [inst_4 : SMulZeroClass α β] [PosSMulReflectLE α β] [inst_6 : FloorDiv α β]
  [inst_7 : CeilDiv α β] {a : α} {b : β}, b ⌊/⌋ a ≤ b ⌈/⌉ a

Defined in

Mathlib.Algebra.Order.Floor.Div

Cited by

0 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext

Assumes

AddCommMonoidLinearOrderAddCommMonoidPartialOrderSMulZeroClassPosSMulReflectLEFloorDivCeilDiv