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Theorems · Theorem · ring theory

SkewMonoidAlgebra.single_add_erase

∀ {M : Type u_4} {α : Type u_5} [inst : AddCommMonoid M] (a : α) (f : SkewMonoidAlgebra M α),
  SkewMonoidAlgebra.single a (f.coeff a) + (SkewMonoidAlgebra.erase a) f = f
Defined in
Mathlib.Algebra.SkewMonoidAlgebra.Single
Cited by
2 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoid
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Around this declaration

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

SkewMonoidAlgebra.induction · cited by 1SkewMonoidAlgebra.inducti…SkewPolynomial.monomial_add_erase · cited by 0SkewPolynomial.monomial_a…DFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidFinsupp · cited by 5255FinsuppAddMonoidHom · cited by 3230AddMonoidHomFinsupp.single · cited by 943Finsupp.singleSkewMonoidAlgebra · cited by 216SkewMonoidAlgebraSkewMonoidAlgebra.coeff · cited by 110SkewMonoidAlgebra.coeffSkewMonoidAlgebra.single · cited by 83SkewMonoidAlgebra.singleSkewMonoidAlgebra.erase · cited by 12SkewMonoidAlgebra.eraseSkewMonoidAlgebra.ext · cited by 10SkewMonoidAlgebra.extFinsupp.single_add_erase · cited by 6Finsupp.single_add_eraseSkewMonoidAlgebra.coeff_add · cited by 6SkewMonoidAlgebra.coeff_a…SkewMonoidAlgebra.coeff_erase_apply · cited by 4SkewMonoidAlgebra.coeff_e…SkewMonoidAlgebra.single_add_…CITED BYCITES

Cites13

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Cited by2

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