Theorems · Theorem · order theory
pos_iff_ne_zero
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : Zero α] [IsBotZeroClass α], 0 < a ↔ a ≠ 0- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 180 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 26 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- zero_leproof · cited by 382
- IsBotZeroClassstatement and proof · cited by 71
- LE.le.lt_iff_neproof · cited by 34
Cited by180
Results whose statement or proof uses this declaration.
- Complex.exp_addproof · cited by 55
- Order.one_le_iff_ne_zeroproof · cited by 32
- zero_lt_iffproof · cited by 29
- ENNReal.lt_add_rightproof · cited by 27
- Ordinal.opow_posproof · cited by 22
- pos_of_ne_zeroproof · cited by 21
- MeasureTheory.lintegral_eq_zero_iff'proof · cited by 16
- Cardinal.one_le_iff_ne_zeroproof · cited by 14
- Nat.totient_prime_powproof · cited by 13
- Set.ncard_posproof · cited by 11
- Ordinal.opow_ne_zeroproof · cited by 10
- addOrderOf_pos_iffproof · cited by 10