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Theorems · Theorem · order theory

Order.Ideal.IsPrime.compl_filter

∀ {P : Type u_1} {inst : Preorder P} {I : Order.Ideal P} [self : I.IsPrime], Order.IsPFilter (↑I)ᶜ
Defined in
Mathlib.Order.PrimeIdeal
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses Quot.sound
Assumes
Order.Ideal.IsPrime
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.Ideal.IsPrime.mem_or_mem · cited by 2IsPrime.mem_or_memOrder.Ideal.IsPrime.toPrimePair · cited by 0IsPrime.toPrimePairSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coePreorder · cited by 7952PreorderCompl.compl · cited by 2925Compl.complOrder.Ideal · cited by 102Order.IdealOrder.Ideal.IsPrime · cited by 11Ideal.IsPrimeOrder.IsPFilter · cited by 6Order.IsPFilterIsPrime.compl_filterCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.