Theorems · Theorem · commutative algebra
MvPolynomial.optionEquivLeft_apply
∀ (R : Type u) (S₁ : Type v) [inst : CommSemiring R] (a : MvPolynomial (Option S₁) R),
(MvPolynomial.optionEquivLeft R S₁) a =
(MvPolynomial.aeval fun o => o.elim Polynomial.X fun s => Polynomial.C (MvPolynomial.X s)) a- Defined in
- Mathlib.Algebra.MvPolynomial.Equiv
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- AlgEquivstatement · cited by 1,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.aevalstatement · cited by 298
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.optionEquivLeft_X_noneproof · cited by 3
- MvPolynomial.optionEquivLeft_Cproof · cited by 2
- MvPolynomial.optionEquivLeft_X_someproof · cited by 2
- MvPolynomial.finSuccEquiv_eqproof · cited by 1
- MvPolynomial.finSuccEquiv_rename_finSuccEquivproof · cited by 1
- MvPolynomial.optionEquivLeft_elim_evalproof · cited by 1
- MvPolynomial.optionEquivLeft_monomialproof · cited by 1