Theorems · Theorem · order theory
le_of_smul_le_smul_of_pos_left
∀ {α : Type u_1} {β : Type u_2} {a : α} {b₁ b₂ : β} [inst : SMul α β] [inst_1 : Preorder α] [inst_2 : Preorder β]
[inst_3 : Zero α] [PosSMulReflectLE α β], a • b₁ ≤ a • b₂ → 0 < a → b₁ ≤ b₂Alias of le_of_smul_le_smul_left.
- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 3 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
- PosSMulReflectLEstatement · cited by 51
- le_of_smul_le_smul_leftproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- nonpos_of_smul_nonpos_of_pos_leftproof · cited by 1
- nonneg_of_smul_nonneg_of_pos_leftproof · cited by 1
- le_of_smul_le_smul_of_negproof · cited by 0