Theorems · Theorem · field theory

IsAlgClosure.equivOfEquiv.congr_simp

∀ {R : Type u} {S : Type u_3} (L : Type v) (M : Type w) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Field L]
  [inst_3 : Field M] [inst_4 : Algebra R M] [inst_5 : Module.IsTorsionFree R M] [inst_6 : IsAlgClosure R M]
  [inst_7 : Algebra S L] [inst_8 : Module.IsTorsionFree S L] [inst_9 : IsAlgClosure S L] [inst_10 : IsDomain R]
  [inst_11 : IsDomain S] (hSR hSR_1 : S ≃+* R),
  hSR = hSR_1 → IsAlgClosure.equivOfEquiv L M hSR = IsAlgClosure.equivOfEquiv L M hSR_1

Defined in: Mathlib.FieldTheory.IsAlgClosed.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Field Field Algebra Module.IsTorsionFree IsAlgClosure Algebra Module.IsTorsionFree IsAlgClosure IsDomain IsDomain

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CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
IsDomainstatement and proof · cited by 2,196
RingEquivstatement and proof · cited by 1,147
Module.IsTorsionFreestatement and proof · cited by 600
IsAlgClosurestatement and proof · cited by 16
IsAlgClosure.equivOfEquivstatement and proof · cited by 5

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