Theorems · Theorem · order theory
smul_lt_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] [PosSMulStrictMono α β], b₁ < b₂ → 0 < a → a • b₁ < a • b₂- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 23 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 and proof · cited by 7,952
- PosSMulStrictMonostatement and proof · cited by 128
- strictMono_smul_left_of_posproof · cited by 3
Cited by23
Results whose statement or proof uses this declaration.
- smul_lt_smul_iff_of_pos_leftproof · cited by 8
- convex_Iioproof · cited by 6
- smul_posproof · cited by 5
- Finset.expect_lt_expectproof · cited by 4
- ConvexOn.le_left_of_right_le'proof · cited by 3
- StrictConvexOn.map_sum_ltproof · cited by 3
- ConvexOn.lt_left_of_right_lt'proof · cited by 3
- ConvexOn.convex_ltproof · cited by 3
- openSegment_subset_Iooproof · cited by 2
- starConvex_compl_Iicproof · cited by 2
- smul_add_smul_lt_smul_add_smulproof · cited by 2
- ConvexOn.openSegment_subset_strict_epigraphproof · cited by 2