Theorems · Theorem · order theory
inv_smul_le_iff_of_pos
∀ {α : Type u_1} {β : Type u_2} {a : α} {b₁ b₂ : β} [inst : GroupWithZero α] [inst_1 : Preorder α] [inst_2 : Preorder β]
[inst_3 : MulAction α β] [PosSMulMono α β] [PosSMulReflectLE α β], 0 < a → (a⁻¹ • b₁ ≤ b₂ ↔ b₁ ≤ a • b₂)- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LT.lt.ne'proof · cited by 1,417
- MulActionstatement and proof · cited by 1,294
- GroupWithZerostatement and proof · cited by 691
- PosSMulMonostatement and proof · cited by 188
- smul_inv_smul₀proof · cited by 59
- PosSMulReflectLEstatement and proof · cited by 51
- smul_le_smul_iff_of_pos_leftproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- map_le_lineMap_iff_slope_le_slope_leftproof · cited by 3
- Finset.centerMass_le_supproof · cited by 2
- Finset.expect_leproof · cited by 1