Theorems · Theorem · number theory
one_le_two
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : LE α] [ZeroLEOneClass α] [AddLeftMono α], 1 ≤ 2- Defined in
- Mathlib.Algebra.Order.Monoid.NatCast
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 19 from the axioms · 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.
- add_zeroproof · cited by 2,707
- AddLeftMonostatement and proof · cited by 687
- zero_le_oneproof · cited by 316
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- one_add_one_eq_twoproof · cited by 65
- add_le_add_rightproof · cited by 37
Cited by44
Results whose statement or proof uses this declaration.
- zero_lt_twoproof · cited by 124
- Real.sin_pi_over_two_pow_succproof · cited by 6
- Polynomial.degree_quadratic_leproof · cited by 4
- ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExpproof · cited by 3
- Collinear.coplanarproof · cited by 3
- Real.lt_tanproof · cited by 2
- EuclideanSpace.volume_ballproof · cited by 2
- midpoint_le_midpointproof · cited by 2
- ProbabilityTheory.variance_add_constproof · cited by 2
- Nat.le_fib_add_oneproof · cited by 2
- SimpleGraph.IsAcyclic.of_subsingletonproof · cited by 2
- Chebyshev.psi_ge'proof · cited by 2