Theorems · Theorem · commutative algebra
Algebra.SubmersivePresentation.basisKaehlerOfIsCompl.congr_simp
∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
[inst_2 : Algebra R S] [inst_3 : Finite σ] (P P_1 : Algebra.SubmersivePresentation R S ι σ) (e_P : P = P_1)
{κ : Type u_5} {f f_1 : κ → ι} (e_f : f = f_1) (hf : Function.Injective f)
(hcompl : IsCompl (Set.range f) (Set.range P.map)), P.basisKaehlerOfIsCompl hf hcompl = P_1.basisKaehlerOfIsCompl ⋯ ⋯- Cited by
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- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.rangestatement and proof · cited by 4,705
- Finitestatement and proof · cited by 3,029
- Module.Basisstatement · cited by 1,477
- IsComplstatement and proof · cited by 351
- KaehlerDifferentialstatement · cited by 204
- Algebra.SubmersivePresentationstatement and proof · cited by 52
- Algebra.SubmersivePresentation.toPreSubmersivePresentationstatement and proof · cited by 47
- Algebra.PreSubmersivePresentation.mapstatement and proof · cited by 34
- Algebra.SubmersivePresentation.basisKaehlerOfIsComplstatement and proof · cited by 2
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