Theorems · Theorem · field theory
RatFunc.taylor_mem_nonZeroDivisors
∀ {R : Type u} [inst : CommRing R] (r : R),
∀ p ∈ nonZeroDivisors (Polynomial R), (Polynomial.taylor r) p ∈ nonZeroDivisors (Polynomial R)- Defined in
- Mathlib.FieldTheory.Laurent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Submonoidstatement · cited by 3,086
- sub_eq_add_negproof · cited by 1,023
- sub_selfproof · cited by 996
- nonZeroDivisorsstatement and proof · cited by 895
- Polynomial.taylorstatement and proof · cited by 42
- LinearMap.map_eq_zero_iffproof · cited by 10
- mem_nonZeroDivisors_iff_rightproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- RatFunc.laurentproof · cited by 7
- RatFunc.laurentAuxproof · cited by 3
- RatFunc.laurentAux_divproof · cited by 2
- RatFunc.laurentAux_ofFractionRing_mkstatement and proof · cited by 0