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Theorems · Theorem · general algebraic systems

natCast_apply

∀ {F : Type u_1} {α : outParam (Type u_2)} {inst : FunLike F α α} {inst_1 : NatCast F} {inst_2 : SMul ℕ α}
  [self : IsNatCastApply F α] (n : ℕ) (x : α), ↑n x = n • x

Alias of IsNatCastApply.natCast_apply.

Defined in
Mathlib.Data.FunLike.IsApply
Cited by
1 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
IsNatCastApply
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FunLike.natCast_eq_nsmul_one · cited by 1FunLike.natCast_eq_nsmul_…DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeIsNatCastApply · cited by 4IsNatCastApplyIsNatCastApply.natCast_apply · cited by 1IsNatCastApply.natCast_ap…natCast_applyCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.