Theorems · Theorem · commutative algebra
Nat.cast_ne_zero
∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R] {n : ℕ}, ↑n ≠ 0 ↔ n ≠ 0- Defined in
- Mathlib.Algebra.CharZero.Defs
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 40 definitions · uses propext
- Assumes
- AddMonoidWithOneCharZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CharZerostatement and proof · cited by 932
- AddMonoidWithOnestatement and proof · cited by 313
- Nat.cast_eq_zeroproof · cited by 18
Cited by113
Results whose statement or proof uses this declaration.
- Complex.exp_addproof · cited by 55
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- OfNat.ofNat_ne_zeroproof · cited by 20
- Rat.cast_addproof · cited by 19
- Rat.cast_mulproof · cited by 19
- Rat.cast_subproof · cited by 9
- Nat.cast_chooseproof · cited by 6
- NNRat.cast_mulproof · cited by 5
- Rat.cast_injectiveproof · cited by 5
- Complex.Gamma_nat_eq_factorialproof · cited by 4
- Complex.Gamma_neg_nat_eq_zeroproof · cited by 4
- ENat.zero_epowproof · cited by 4