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Theorems · Theorem · group theory

Pi.single_mul

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : (i : ι) → MulZeroClass (α i)] [inst_1 : DecidableEq ι] (i : ι) (x y : α i),
  Pi.single i (x * y) = Pi.single i x * Pi.single i y
Defined in
Mathlib.Algebra.GroupWithZero.Pi
Cited by
3 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
MulZeroClassDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Algebra.FormallySmooth.pi_iff · cited by 1FormallySmooth.pi_iffAlgebra.FormallyUnramified.pi_iff · cited by 1FormallyUnramified.pi_iffAlgebra.FormallySmooth.of_pi · cited by 1FormallySmooth.of_piPi.single · cited by 518Pi.singleMulZeroClass · cited by 232MulZeroClassMulHom.single · cited by 2MulHom.singleMulHom.map_mul · cited by 1MulHom.map_mulPi.single_mulCITED BYCITES

Cites4

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

Cited by3

Results whose statement or proof uses this declaration.