Theorems · Theorem · commutative algebra
Polynomial.toSubring.congr_simp
∀ {R : Type u_1} [inst : Ring R] (p p_1 : Polynomial R) (e_p : p = p_1) (T : Subring R) (hp : ↑p.coeffs ⊆ ↑T),
p.toSubring T hp = p_1.toSubring T ⋯- Defined in
- Mathlib.RingTheory.Polynomial.Subring
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Subringstatement and proof · cited by 602
- Polynomial.coeffsstatement and proof · cited by 41
- Polynomial.toSubringstatement and proof · cited by 15
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