Theorems · Theorem · general algebraic systems
Function.support_eq_univ
∀ {ι : Type u_1} {M : Type u_3} [inst : Zero M] {f : ι → M}, (∀ (x : ι), f x ≠ 0) → Function.support f = Set.univThe support of a function that is everywhere nonzero is the whole space.
- Defined in
- Mathlib.Algebra.Notation.Support
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement · cited by 3,945
- Function.supportstatement · cited by 610
- Set.eq_univ_of_forallproof · cited by 80
Cited by2
Results whose statement or proof uses this declaration.
- Function.support_mul_of_ne_zero_leftproof · cited by 0
- Function.support_mul_of_ne_zero_rightproof · cited by 0