Theorems · Theorem · algebraic geometry
AlgebraicGeometry.StructureSheaf.const.congr_simp
∀ {R M : Type u} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f f_1 : M),
f = f_1 →
∀ (g g_1 : R) (e_g : g = g_1) (U : TopologicalSpace.Opens ↑(AlgebraicGeometry.PrimeSpectrum.Top R))
(hu : U ≤ PrimeSpectrum.basicOpen g),
AlgebraicGeometry.StructureSheaf.const f g U hu = AlgebraicGeometry.StructureSheaf.const f_1 g_1 U ⋯- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CategoryTheory.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- AddCommGroupstatement and proof · cited by 12,871
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
- Opens.grothendieckTopologystatement · cited by 206
- PrimeSpectrum.basicOpenstatement and proof · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.const_oneproof · cited by 0