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Theorems · Theorem · group theory

Finset.coe_smul

∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq β] [inst_1 : SMul α β] (s : Finset α) (t : Finset β),
  ↑(s • t) = ↑s • ↑t
Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Scalar
Cited by
6 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CovBySMul.trans · cited by 2CovBySMul.transSubmodule.FG.smul · cited by 2FG.smulFinset.zero_mem_smul_iff · cited by 0Finset.zero_mem_smul_iffFinset.smul_univ · cited by 0Finset.smul_univFinset.smul_univ₀ · cited by 0Finset.smul_univ₀Finset.smul_univ₀' · cited by 0Finset.smul_univ₀'Set · cited by 53352SetFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeSet.smul · cited by 110Set.smulFinset.coe_image₂ · cited by 55Finset.coe_image₂Finset.smul · cited by 45Finset.smulFinset.coe_smulCITED BYCITES

Cites6

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

Cited by6

Results whose statement or proof uses this declaration.