Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ord_le_smul
∀ {X : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsIntegral X]
[inst_1 : AlgebraicGeometry.IsLocallyNoetherian X] {x : ↥X} {U : X.Opens} [inst_2 : Nonempty ↥↑U],
x ∈ U →
∀ {a : ↑(X.presheaf.obj (Opposite.op U))},
a ≠ 0 → ∀ (f : ↑X.functionField), AlgebraicGeometry.Scheme.ord f x ≤ AlgebraicGeometry.Scheme.ord (a • f) x- Cited by
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- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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