Theorems · Theorem · commutative algebra
Nat.cast_succ
∀ {R : Type u_1} [inst : AddMonoidWithOne R] (n : ℕ), ↑n.succ = ↑n + 1- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 99 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 35 definitions · uses no axioms
- Assumes
- AddMonoidWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidWithOnestatement and proof · cited by 313
- AddMonoidWithOne.natCast_succproof · cited by 2
Cited by99
Results whose statement or proof uses this declaration.
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_addproof · cited by 586
- nsmul_eq_mulproof · cited by 369
- zsmul_eq_mulproof · cited by 120
- Nat.cast_smul_eq_nsmulproof · cited by 110
- Nat.mono_castproof · cited by 76
- Nat.cast_add_oneproof · cited by 56
- Real.log_powproof · cited by 29
- Nat.cast_commuteproof · cited by 24
- Ordinal.opow_natCastproof · cited by 11
- Polynomial.derivative_powproof · cited by 11
- ascPochhammer_succ_rightproof · cited by 11