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Theorems · Theorem · general algebraic systems

Finsupp.single_eq_same

∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] {a : α} {b : M}, (fun₀ | a => b) a = b
Defined in
Mathlib.Data.Finsupp.Single
Cited by
171 results in Mathlib
Foundations
Depth 60 from the axioms, rests on 837 definitions · uses propext, Classical.choice, Quot.sound
Assumes
Zero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finsupp.sum_single_index · cited by 130Finsupp.sum_single_indexPowerSeries.coeff_mk · cited by 47PowerSeries.coeff_mkFinsupp.prod_single_index · cited by 26Finsupp.prod_single_indexPolynomial.coeff_coe · cited by 25Polynomial.coeff_coeFinsupp.mapDomain_apply · cited by 11Finsupp.mapDomain_applyMatrix.toLin_self · cited by 9Matrix.toLin_selfFinsupp.single_injective · cited by 9Finsupp.single_injectivelinearIndependent_iff'ₛ · cited by 9linearIndependent_iff'ₛFinsupp.comapDomain_single · cited by 9Finsupp.comapDomain_singlePolynomial.coeff_monomial_same · cited by 8Polynomial.coeff_monomial…PowerSeries.coeff_derivative · cited by 8PowerSeries.coeff_derivat…MvPolynomial.coeff_zero_C · cited by 7MvPolynomial.coeff_zero_CFinsupp.uncurry_single · cited by 6Finsupp.uncurry_singleModule.Basis.singleton_repr · cited by 6Basis.singleton_reprFinsupp.unique_single · cited by 6Finsupp.unique_singleDFunLike.coe · cited by 62936DFunLike.coeFinsupp · cited by 5255FinsuppFinsupp.single · cited by 943Finsupp.singlePi.single_eq_same · cited by 144Pi.single_eq_sameFinsupp.single_eq_sameCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by171

Results whose statement or proof uses this declaration.