Theorems · Theorem · number theory
zero_lt_two
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],
0 < 2See zero_lt_two' for a version with the type explicit.
- Defined in
- Mathlib.Algebra.Order.Monoid.NatCast
- Cited by
- 124 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 146 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddLeftMonostatement and proof · cited by 687
- LT.lt.trans_leproof · cited by 678
- zero_lt_oneproof · cited by 598
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- one_le_twoproof · cited by 44
Cited by124
Results whose statement or proof uses this declaration.
- half_posproof · cited by 83
- two_posproof · cited by 68
- zero_lt_two'proof · cited by 16
- zero_lt_threeproof · cited by 10
- Path.trans_applystatement and proof · cited by 9
- Real.Gamma_one_half_eqproof · cited by 6
- Real.two_le_piproof · cited by 5
- ZMod.χ₄_eq_neg_one_powproof · cited by 5
- Real.pi_upper_bound_startproof · cited by 5
- Real.norm_twoproof · cited by 4
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- Urysohns.CU.approx_le_oneproof · cited by 4