Theorems · Theorem · commutative algebra
map_natCast
∀ {R : Type u_3} {S : Type u_4} {F : Type u_5} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S]
[inst_2 : FunLike F R S] [RingHomClass F R S] (f : F) (n : ℕ), f ↑n = ↑n- Defined in
- Mathlib.Data.Nat.Cast.Basic
- Cited by
- 134 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 171 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- map_oneproof · cited by 861
- NonAssocSemiringstatement and proof · cited by 805
- RingHomClassstatement and proof · cited by 193
- map_natCast'proof · cited by 4
Cited by134
Results whose statement or proof uses this declaration.
- map_ofNatproof · cited by 73
- NNReal.coe_natCastproof · cited by 34
- Polynomial.derivative_Cproof · cited by 30
- Polynomial.C_eq_natCastproof · cited by 25
- Polynomial.derivative_mapproof · cited by 17
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- map_ratCastproof · cited by 10
- map_wittPolynomialproof · cited by 10
- tendsto_inv_atTop_nhds_zero_natproof · cited by 9
- Polynomial.map_natCastproof · cited by 8
- ZMod.unitsMap_surjectiveproof · cited by 7
- WittVector.frobenius_verschiebungproof · cited by 7