Theorems · Theorem · order theory

OrderIso.smulRight_apply

∀ {α : Type u_1} {β : Type u_2} [inst : GroupWithZero α] [inst_1 : Preorder α] [inst_2 : Preorder β]
  [inst_3 : MulAction α β] [inst_4 : PosSMulMono α β] [inst_5 : PosSMulReflectLE α β] {a : α} (ha : 0 < a) (b : β),
  (OrderIso.smulRight ha) b = a • b

Defined in: Mathlib.Algebra.Order.Module.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: GroupWithZero Preorder Preorder MulAction PosSMulMono PosSMulReflectLE

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DFunLike.coestatement and proof · cited by 62,936
Preorderstatement and proof · cited by 7,952
MulActionstatement and proof · cited by 1,294
GroupWithZerostatement and proof · cited by 691
RelIsostatement · cited by 456
PosSMulMonostatement and proof · cited by 188
PosSMulReflectLEstatement and proof · cited by 51
OrderIso.smulRightstatement and proof · cited by 8

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