Theorems · Theorem · general algebraic systems
Finsupp.single_eq_single_iff
∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] (a₁ a₂ : α) (b₁ b₂ : M),
((fun₀ | a₁ => b₁) = fun₀ | a₂ => b₂) ↔ a₁ = a₂ ∧ b₁ = b₂ ∨ b₁ = 0 ∧ b₂ = 0- Defined in
- Mathlib.Data.Finsupp.Single
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsuppstatement · cited by 5,255
- Finsupp.singlestatement and proof · cited by 943
- DFunLike.ext_iffproof · cited by 102
- Finsupp.single_injectiveproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Finsupp.single_left_injectiveproof · cited by 5
- AddMonoidAlgebra.single_injproof · cited by 4
- LinearIndependent.eq_of_smul_apply_eq_smul_applyproof · cited by 1
- MvPowerSeries.X_injproof · cited by 0
- SkewPolynomial.monomial_eq_monomial_iffproof · cited by 0
- SkewMonoidAlgebra.of_injectiveproof · cited by 0