Theorems · Theorem · algebraic geometry
AlgebraicGeometry.compact_open_induction_on
∀ {X : AlgebraicGeometry.Scheme} {P : X.Opens → Prop} (S : X.Opens),
IsCompact ↑S → P ⊥ → (∀ (S : X.Opens), IsCompact S.carrier → ∀ (U : ↑X.affineOpens), P S → P (S ⊔ ↑U)) → P S- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- Set.iUnionproof · cited by 2,483
- iSupproof · cited by 2,415
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparatedproof · cited by 1
- AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpensproof · cited by 1