Theorems · Theorem · order theory
lt_inv_smul_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] [PosSMulStrictMono α β] [PosSMulReflectLT α β], 0 < a → (b₁ < a⁻¹ • b₂ ↔ a • b₁ < b₂)- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- PosSMulStrictMonostatement and proof · cited by 128
- smul_inv_smul₀proof · cited by 59
- PosSMulReflectLTstatement and proof · cited by 28
- smul_lt_smul_iff_of_pos_leftproof · cited by 8
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