Theorems · Theorem · number theory
zero_lt_three
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],
0 < 3See zero_lt_three' for a version with the type explicit.
- Defined in
- Mathlib.Algebra.Order.Monoid.NatCast
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- zero_le_oneproof · cited by 316
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- zero_lt_twoproof · cited by 124
- two_add_one_eq_threeproof · cited by 8
- lt_add_of_lt_of_nonnegproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- zero_lt_fourproof · cited by 8
- IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mulproof · cited by 3
- card_support_eq_three_iffproof · cited by 3
- three_posproof · cited by 2
- Real.exp_bound_div_one_sub_of_interval'proof · cited by 2
- zero_lt_three'proof · cited by 2
- Polynomial.X_pow_sub_X_sub_one_irreducible_auxproof · cited by 1
- exists_forall_closed_ball_dist_add_le_two_subproof · cited by 1
- ruzsaSzemerediNumberNat_asymptotic_lower_boundproof · cited by 0