Theorems · Theorem · field theory
Polynomial.mem_map_rangeS
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S) {p : Polynomial S},
p ∈ (Polynomial.mapRingHom f).rangeS ↔ ∀ (n : ℕ), p.coeff n ∈ f.rangeS- Defined in
- Mathlib.Algebra.Polynomial.Eval.Subring
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.mapproof · cited by 806
- Subsemiringstatement · cited by 456
- Set.mem_range_selfproof · cited by 328
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.lifts_iff_coeff_liftsproof · cited by 10
- Polynomial.notMem_map_rangeSproof · cited by 1
- Polynomial.erase_mem_liftsproof · cited by 0
- Polynomial.mem_map_rangeproof · cited by 0