Theorems · Theorem · order theory

smul_pos_iff_of_pos_left

∀ {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] [PosSMulReflectLT α β],
  0 < a → (0 < a • b ↔ 0 < b)

Defined in: Mathlib.Algebra.Order.Module.Defs
Cited by: 0 results in Mathlib
Foundations: Depth 8 from the axioms · uses no axioms
Assumes: Zero Zero SMulZeroClass Preorder Preorder PosSMulStrictMono PosSMulReflectLT

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Preorderstatement and proof · cited by 7,952
smul_zeroproof · cited by 665
SMulZeroClassstatement and proof · cited by 213
PosSMulStrictMonostatement and proof · cited by 128
PosSMulReflectLTstatement and proof · cited by 28
smul_lt_smul_iff_of_pos_leftproof · cited by 8

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