mathlib
ccc1431c - feat(ring_theory/ideal_operations): prime avoidance (#773)

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5 years ago
feat(ring_theory/ideal_operations): prime avoidance (#773) ```lean /-- Prime avoidance. Atiyah-Macdonald 1.11, Eisenbud 3.3, Stacks 10.14.2 (00DS), Matsumura Ex.1.6. -/ theorem subset_union_prime {s : finset ι} {f : ι → ideal R} (a b : ι) (hp : ∀ i ∈ s, i ≠ a → i ≠ b → is_prime (f i)) {I : ideal R} : (I : set R) ⊆ (⋃ i ∈ (↑s : set ι), f i) ↔ ∃ i ∈ s, I ≤ f i := ``` Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com> Co-authored-by: Ms2ger <Ms2ger@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>
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