Theorems · Theorem · order theory
inv_pos
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a : G₀}, 0 < a⁻¹ ↔ 0 < a- Cited by
- 124 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 176 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- mul_oneproof · cited by 3,885
- LT.lt.leproof · cited by 2,189
- MulZeroClass.mul_zeroproof · cited by 2,091
- LT.lt.ne'proof · cited by 1,417
- GroupWithZerostatement and proof · cited by 691
- inv_invproof · cited by 494
- PosMulReflectLTstatement and proof · cited by 278
- mul_inv_cancel₀proof · cited by 210
- lt_of_mul_lt_mul_leftproof · cited by 15
Cited by124
Results whose statement or proof uses this declaration.
- div_posproof · cited by 337
- Real.exp_posproof · cited by 169
- inv_pos_of_posproof · cited by 123
- one_div_posproof · cited by 27
- zpow_posproof · cited by 22
- Real.HolderTriple.pos'proof · cited by 13
- inv_lt_comm₀proof · cited by 11
- inv_lt_zero'proof · cited by 11
- div_neg_of_neg_of_posproof · cited by 9
- Filter.tendsto_const_mul_atTop_of_posproof · cited by 8
- lt_inv_comm₀proof · cited by 8
- inv_le_comm₀proof · cited by 8