Theorems · Theorem · order theory
le_of_smul_le_smul_of_pos_right
∀ {α : Type u_1} {β : Type u_2} {a₁ a₂ : α} {b : β} [inst : SMul α β] [inst_1 : Preorder α] [inst_2 : Preorder β]
[inst_3 : Zero β] [SMulPosReflectLE α β], a₁ • b ≤ a₂ • b → 0 < b → a₁ ≤ a₂Alias of le_of_smul_le_smul_right.
- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- SMulPosReflectLEstatement · cited by 16
- le_of_smul_le_smul_rightproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.isPositive_smul_iffproof · cited by 1
- SMulPosReflectLE.toSMulPosStrictMonoproof · cited by 1
- nonneg_of_smul_nonneg_of_pos_rightproof · cited by 1
- nonpos_of_smul_nonpos_of_pos_rightproof · cited by 1