Theorems · Theorem · order theory

gc_smul_ceilDiv

∀ {α : Type u_2} {β : Type u_3} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [inst_4 : SMulZeroClass α β] [inst_5 : CeilDiv α β] {a : α},
  0 < a → GaloisConnection (fun x => x ⌈/⌉ a) fun x => a • x

Defined in

Mathlib.Algebra.Order.Floor.Div

Cited by

2 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

AddCommMonoidPartialOrderAddCommMonoidPartialOrderSMulZeroClassCeilDiv