Theorems · Theorem · field theory
RatFunc.mk_eq_mk
∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] {p q p' q' : Polynomial K},
q ≠ 0 → q' ≠ 0 → (RatFunc.mk p q = RatFunc.mk p' q' ↔ p * q' = p' * q)- Defined in
- Mathlib.FieldTheory.RatFunc.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- IsDomainstatement and proof · cited by 2,196
- RatFuncstatement and proof · cited by 301
- IsLocalization.mk'proof · cited by 218
- FractionRingproof · cited by 200
- IsFractionRing.injectiveproof · cited by 70
- mem_nonZeroDivisors_iff_ne_zeroproof · cited by 38
- RatFunc.mkstatement and proof · cited by 21
- RatFunc.ofFractionRing_injectiveproof · cited by 3
- RatFunc.mk_def_of_neproof · cited by 2
- IsLocalization.mk'_eq_iff_eq'proof · cited by 2
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