Theorems · Theorem · field theory
Polynomial.mem_map_range
∀ {R : Type u_1} {S : Type u_2} [inst : Ring R] [inst_1 : Ring S] (f : R →+* S) {p : Polynomial S},
p ∈ (Polynomial.mapRingHom f).range ↔ ∀ (n : ℕ), p.coeff n ∈ f.range- Defined in
- Mathlib.Algebra.Polynomial.Eval.Subring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- Subringstatement · cited by 602
- RingHom.rangestatement · cited by 138
- Polynomial.mapRingHomstatement · cited by 98
- Polynomial.mem_map_rangeSproof · cited by 4
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