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Theorems · Theorem · field theory

RatFunc.mk_zero

∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] (p : Polynomial K), RatFunc.mk p 0 = { toFractionRing := 0 }
Defined in
Mathlib.FieldTheory.RatFunc.Defs
Cited by
2 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDomain
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RatFunc.liftOn_mk · cited by 2RatFunc.liftOn_mkRatFunc.mk_smul · cited by 1RatFunc.mk_smulDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingPolynomial · cited by 5681PolynomialAlgebra.algebraMap · cited by 4706Algebra.algebraMapIsDomain · cited by 2196IsDomainmap_zero · cited by 1614map_zerononZeroDivisors · cited by 895nonZeroDivisorsRatFunc · cited by 301RatFuncdiv_zero · cited by 251div_zeroFractionRing · cited by 200FractionRingRatFunc.mk · cited by 21RatFunc.mkRatFunc.mk_eq_div' · cited by 4RatFunc.mk_eq_div'RatFunc.mk_zeroCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.