Theorems · Theorem · general algebraic systems
Finsupp.smul_single_one
∀ {α : Type u_1} {R : Type u_6} [inst : MulZeroOneClass R] (a : α) (b : R), (b • fun₀ | a => 1) = fun₀ | a => b- Defined in
- Mathlib.Data.Finsupp.SMul
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulZeroOneClass
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.
- Finsuppstatement and proof · cited by 5,255
- mul_oneproof · cited by 3,885
- Finsupp.singlestatement and proof · cited by 943
- smul_eq_mulproof · cited by 357
- MulZeroOneClassstatement and proof · cited by 184
- Finsupp.smul_singleproof · cited by 48
Cited by7
Results whose statement or proof uses this declaration.
- KaehlerDifferential.kerTotal_mkQ_single_algebraMapproof · cited by 2
- toMatrix_distrib_mul_action_toLinearMapproof · cited by 1
- KaehlerDifferential.kerTotal_mkQ_single_mulproof · cited by 1
- IsModuleTopology.continuous_bilinear_of_pi_fintypeproof · cited by 1
- Finsupp.range_lmapDomainproof · cited by 1
- KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombinationproof · cited by 1
- KaehlerDifferential.kerTotal_mkQ_single_addproof · cited by 0