Theorems · Theorem · order theory
PosSMulReflectLT.lt_of_smul_lt_smul_left
∀ {α : Type u_1} {β : Type u_2} {inst : SMul α β} {inst_1 : Preorder α} {inst_2 : Preorder β} {inst_3 : Zero α}
[self : PosSMulReflectLT α β] ⦃a : α⦄, 0 ≤ a → ∀ ⦃b₁ b₂ : β⦄, a • b₁ < a • b₂ → b₁ < b₂Do not use this. Use lt_of_smul_lt_smul_left instead.
- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- PosSMulReflectLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- PosSMulReflectLTstatement and proof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- lt_of_smul_lt_smul_leftproof · cited by 7