Theorems · Theorem · commutative algebra
nsmul_one
∀ {A : Type u_2} [inst : AddMonoidWithOne A] (n : ℕ), n • 1 = ↑n- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- AddMonoidWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidWithOnestatement and proof · cited by 313
Cited by34
Results whose statement or proof uses this declaration.
- exists_nat_gtproof · cited by 26
- zsmul_oneproof · cited by 26
- exists_nat_geproof · cited by 20
- ENNReal.tsum_geometricproof · cited by 8
- Nat.cast_card_eq_zeroproof · cited by 8
- CoxeterSystem.lengthParity_eq_ofAdd_lengthproof · cited by 5
- CharZero.of_moduleproof · cited by 4
- IsNonarchimedean.apply_natCast_le_oneproof · cited by 3
- LaurentSeries.valuation_X_powproof · cited by 3
- AddConstMapClass.map_add_nat'proof · cited by 3
- AddConstMapClass.map_nat_add'proof · cited by 2
- MvPolynomial.supDegree_esymmAlgHomMonomialproof · cited by 2