Theorems · Theorem · general algebraic systems
Finsupp.zero_apply
∀ {α : Type u_1} {M : Type u_4} [inst : Zero M] {a : α}, 0 a = 0- Defined in
- Mathlib.Data.Finsupp.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 59 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.
- DFunLike.coestatement · cited by 62,936
- Finsuppstatement · cited by 5,255
Cited by10
Results whose statement or proof uses this declaration.
- MvPolynomial.isHomogeneous_Cproof · cited by 7
- LinearMap.IsOrthoᵢ.separatingLeft_of_not_isOrtho_basis_selfproof · cited by 2
- Pi.basis_repr_singleproof · cited by 1
- eq_bot_of_generator_maximal_submoduleImage_eq_zeroproof · cited by 1
- LinearMap.singularValues_zeroproof · cited by 1
- Nat.Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponentproof · cited by 1
- Nat.Prime.exists_orderOf_eq_pow_factorization_exponentproof · cited by 1
- LinearMap.singularValues_eq_zero_iffproof · cited by 0
- eq_bot_of_generator_maximal_map_eq_zeroproof · cited by 0
- Module.basisUnique_repr_eq_zero_iffproof · cited by 0