Theorems · Theorem · general algebraic systems
Function.mulSupport_eq_empty_iff
∀ {ι : Type u_1} {M : Type u_3} [inst : One M] {f : ι → M}, Function.mulSupport f = ∅ ↔ f = 1- Defined in
- Mathlib.Algebra.Notation.Support
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- One
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
- Function.mulSupportstatement · cited by 240
- Set.subset_empty_iffproof · cited by 40
- Function.mulSupport_subset_iff'proof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Function.mulSupport_oneproof · cited by 5
- Function.mulSupport_nonempty_iffproof · cited by 0
- mulTSupport_eq_empty_iffproof · cited by 0
- Subsingleton.mulSupport_eqproof · cited by 0