Theorems · Theorem · commutative algebra
Nat.cast_zero
∀ {R : Type u_1} [inst : AddMonoidWithOne R], ↑0 = 0- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 1,870 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 31 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_zeroproof · cited by 2
Cited by1,873
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
- Nat.cast_mulproof · cited by 309
- Nat.cast_nonneg'proof · cited by 245
- Nat.cast_pos'proof · cited by 219
- Int.cast_zeroproof · cited by 188
- Int.cast_mulproof · cited by 113
- Nat.cast_smul_eq_nsmulproof · cited by 110
- Real.two_pi_posproof · cited by 51
- Cardinal.lift_natCastproof · cited by 39
- ENNReal.mul_inv_cancelproof · cited by 37
Showing the 200 most cited of 1,873.