Theorems · Theorem · order theory
Nat.strictMono_cast
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α],
StrictMono Nat.cast- Defined in
- Mathlib.Data.Nat.Cast.Order.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CharZerostatement and proof · cited by 932
- StrictMonostatement · cited by 706
- AddLeftMonostatement and proof · cited by 687
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- Nat.mono_castproof · cited by 76
- Nat.cast_injectiveproof · cited by 39
- Monotone.strictMono_of_injectiveproof · cited by 22
Cited by13
Results whose statement or proof uses this declaration.
- Nat.cast_leproof · cited by 159
- Nat.cast_ltproof · cited by 80
- Nat.castOrderEmbeddingproof · cited by 13
- Cardinal.ofENat_strictMonoproof · cited by 4
- Polynomial.Chebyshev.strictAntiOn_nodeproof · cited by 2
- Polynomial.Chebyshev.isLocalMax_T_realproof · cited by 1
- Polynomial.Chebyshev.isLocalMin_T_realproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_leproof · cited by 1
- ENat.isEmbedding_natCastproof · cited by 1
- ENat.map_natCast_strictMonoproof · cited by 1
- Finset.dens_lt_densproof · cited by 1