Theorems · Theorem · order theory
Set.inv_Ioo_0_left
∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] [MulPosReflectLT G₀]
{a : G₀}, 0 < a → (Set.Ioo 0 a)⁻¹ = Set.Ioi a⁻¹The (pre)image under inv of Ioo 0 a is Ioi a⁻¹.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.extproof · cited by 2,266
- Set.Ioistatement and proof · cited by 1,463
- Set.Ioostatement and proof · cited by 1,214
- GroupWithZerostatement and proof · cited by 691
- LT.lt.transproof · cited by 370
- PosMulReflectLTstatement and proof · cited by 278
- Set.invstatement · cited by 132
- inv_posproof · cited by 124
- MulPosReflectLTstatement and proof · cited by 93
- inv_lt_of_inv_lt₀proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- NormedField.exists_norm_ltproof · cited by 11
- Cardinal.mk_Ioo_realproof · cited by 5
- Set.inv_Ioi₀proof · cited by 2