Theorems · Theorem · field theory
RatFunc.liftMonoidWithZeroHom.congr_simp
∀ {G₀ : Type u_1} {R : Type u_3} [inst : CommGroupWithZero G₀] [inst_1 : CommRing R] (φ φ_1 : Polynomial R →*₀ G₀)
(e_φ : φ = φ_1) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors G₀)),
RatFunc.liftMonoidWithZeroHom φ hφ = RatFunc.liftMonoidWithZeroHom φ_1 ⋯- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZeroCommRing
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZeroHomstatement and proof · cited by 704
- RatFuncstatement · cited by 301
- Submonoid.comapstatement and proof · cited by 179
- CommGroupWithZerostatement and proof · cited by 94
- RatFunc.liftMonoidWithZeroHomstatement and proof · cited by 6
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