Theorems · Theorem · general algebraic systems
Finsupp.single_eq_pi_single
∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] [inst_1 : DecidableEq α] (a : α) (b : M),
(⇑fun₀ | a => b) = Pi.single a b- Defined in
- Mathlib.Data.Finsupp.Single
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Finsupp.singlestatement · cited by 943
- Pi.singlestatement · cited by 518
- Finsupp.single_applyproof · cited by 99
- Pi.single_applyproof · cited by 78
Cited by15
Results whose statement or proof uses this declaration.
- Finsupp.univ_sum_singleproof · cited by 6
- Finsupp.equivFunOnFinite_singleproof · cited by 3
- IsAdjoinRootMonic.coeff_root_powproof · cited by 2
- toMatrix_distrib_mul_action_toLinearMapproof · cited by 1
- toMatrix_dualTensorHomproof · cited by 1
- Pi.counit_comp_finsuppLcoeFunproof · cited by 1
- Finsupp.single_add_single_eq_single_add_singleproof · cited by 1
- associated_norm_prod_smithproof · cited by 1
- Finsupp.lcoeFun_comp_lsingleproof · cited by 1
- Pi.comul_comp_finsuppLcoeFunproof · cited by 1
- Module.Basis.SmithNormalForm.toAddSubgroup_index_eq_pow_mul_prodproof · cited by 1
- Finsupp.single_eq_updateproof · cited by 1