Theorems · Theorem · general algebraic systems
Function.support_extend_zero
∀ {ι : Type u_1} {κ : Type u_2} {N : Type u_4} [inst : Zero N] {f : ι → κ} {g : ι → N},
Function.Injective f → Function.support (Function.extend f g 0) = f '' Function.support g- Defined in
- Mathlib.Algebra.Notation.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- Function.supportstatement and proof · cited by 610
- LE.le.antisymmproof · cited by 507
- Function.extendstatement · cited by 111
- Function.Injective.extend_applyproof · cited by 57
- Function.mem_supportproof · cited by 54
- Function.support_extend_zero_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HasCompactSupport.tsupport_extend_zeroproof · cited by 0