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Theorems · Theorem · ring theory

DirectSum.of_natCast

∀ {ι : Type u_1} [inst : DecidableEq ι] (A : ι → Type u_2) [inst_1 : (i : ι) → AddCommMonoid (A i)]
  [inst_2 : AddMonoid ι] [inst_3 : DirectSum.GSemiring A] (n : ℕ), (DirectSum.of A 0) ↑n = ↑n
Defined in
Mathlib.Algebra.DirectSum.Ring
Cited by
1 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqAddCommMonoidAddMonoidDirectSum.GSemiring
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Around this declaration

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

DirectSum.of_zero_ofNat · cited by 0DirectSum.of_zero_ofNatDFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidDirectSum · cited by 446DirectSumDirectSum.of · cited by 122DirectSum.ofDirectSum.GSemiring · cited by 39DirectSum.GSemiringDirectSum.of_natCastCITED BYCITES

Cites7

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.