Theorems · Theorem · general algebraic systems
Function.notMem_support
∀ {ι : Type u_1} {M : Type u_3} [inst : Zero M] {f : ι → M} {x : ι}, x ∉ Function.support f ↔ f x = 0- Defined in
- Mathlib.Algebra.Notation.Support
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Function.supportstatement · cited by 610
Cited by29
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.apply_eq_zero_of_notMemproof · cited by 25
- MeasureTheory.convolution_eq_right'proof · cited by 4
- ae_eq_zero_of_integral_contMDiff_smul_eq_zeroproof · cited by 3
- MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_leproof · cited by 3
- exists_compact_iff_hasCompactSupportproof · cited by 3
- support_fderiv_subsetproof · cited by 3
- Function.support_extend_zero_subsetproof · cited by 2
- Function.support_iSupproof · cited by 2
- MeasureTheory.convolution_integrand_bound_right_of_le_of_subsetproof · cited by 2
- MeasureTheory.setIntegral_supportproof · cited by 2
- support_deriv_subsetproof · cited by 2
- BddAbove.convolutionExistsAt'proof · cited by 2