Theorems · Theorem · order theory

smul_pos

∀ {α : Type u_1} {β : Type u_2} {a : α} {b : β} [inst : Zero α] [inst_1 : Zero β] [inst_2 : SMulZeroClass α β]
  [inst_3 : Preorder α] [inst_4 : Preorder β] [PosSMulStrictMono α β], 0 < a → 0 < b → 0 < a • b

Defined in

Mathlib.Algebra.Order.Module.Defs

Cited by

5 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

ZeroZeroSMulZeroClassPreorderPreorderPosSMulStrictMono