Theorems · Theorem · order theory

smul_ceilDiv

∀ {α : Type u_2} {β : Type u_3} [inst : Semiring α] [inst_1 : PartialOrder α] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [inst_4 : MulActionWithZero α β] [inst_5 : CeilDiv α β] {a : α} [PosSMulMono α β]
  [PosSMulReflectLE α β], 0 < a → ∀ (b : β), a • b ⌈/⌉ a = b

Defined in

Mathlib.Algebra.Order.Floor.Div

Cited by

1 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidPartialOrderMulActionWithZeroCeilDivPosSMulMonoPosSMulReflectLE