Mathlib Map

Theorems · Theorem · commutative algebra

IsLocalRing.ResidueField.map.congr_simp

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : IsLocalRing R] [inst_2 : CommRing S]
  [inst_3 : IsLocalRing S] (f f_1 : R →+* S) (e_f : f = f_1) [inst_4 : IsLocalHom f],
  IsLocalRing.ResidueField.map f = IsLocalRing.ResidueField.map f_1
Defined in
Mathlib.RingTheory.LocalRing.ResidueField.Basic
Cited by
2 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsLocalRingCommRingIsLocalRingIsLocalHom
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_id · cited by 1LocallyRingedSpace.residu…AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp · cited by 1LocallyRingedSpace.residu…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomIsLocalRing · cited by 339IsLocalRingIsLocalRing.ResidueField · cited by 156IsLocalRing.ResidueFieldIsLocalHom · cited by 100IsLocalHomIsLocalRing.ResidueField.map · cited by 16ResidueField.mapmap.congr_simpCITED BYCITES

Cites6

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.