Theorems · Theorem · commutative algebra
MvPolynomial.map_injective
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] (f : R →+* S₁),
Function.Injective ⇑f → Function.Injective ⇑(MvPolynomial.map f)- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 10,189
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffproof · cited by 315
- MvPolynomial.mapstatement and proof · cited by 147
- MvPolynomial.coeff_mapproof · cited by 13
Cited by19
Results whose statement or proof uses this declaration.
- wittStructureInt_propproof · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- AlgebraicIndependent.restrictScalarsproof · cited by 3
- WittVector.wittZero_eq_zeroproof · cited by 1
- bind₁_rename_expand_wittPolynomialproof · cited by 1
- WittVector.poly_eq_of_wittPolynomial_bind_eqproof · cited by 1
- WittVector.poly_eq_of_wittPolynomial_bind_eq'proof · cited by 1
- eq_wittStructureIntproof · cited by 1
- WittVector.wittAdd_zeroproof · cited by 1
- WittVector.wittMul_zeroproof · cited by 1
- WittVector.wittOne_pos_eq_zeroproof · cited by 1
- WittVector.wittOne_zero_eq_oneproof · cited by 1