Theorems · Theorem · commutative algebra
Function.support_smul_subset_left
∀ {α : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Zero R] [inst_1 : Zero M] [inst_2 : SMulWithZero R M] (f : α → R)
(g : α → M), Function.support (f • g) ⊆ Function.support f- Defined in
- Mathlib.Algebra.Module.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- ZeroZeroSMulWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- zero_smulproof · cited by 716
- Function.supportstatement and proof · cited by 610
- SMulWithZerostatement and proof · cited by 113
- Pi.smul_apply'proof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- tsupport_smul_subset_leftproof · cited by 5
- Convex.finsum_memproof · cited by 3
- SmoothPartitionOfUnity.contMDiff_finsum_smulproof · cited by 2
- MeasureTheory.tendsto_integral_smul_of_tendsto_average_norm_subproof · cited by 1
- PartitionOfUnity.continuous_finsum_smulproof · cited by 1
- Function.HasFiniteSupport.smul_leftproof · cited by 1
- PMF.integral_eq_tsumproof · cited by 0