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Theorems · Theorem · order theory

IsCoatom.codisjoint_of_ne

∀ {α : Type u_2} [inst : SemilatticeSup α] [inst_1 : OrderTop α] {a b : α},
  IsCoatom a → IsCoatom b → a ≠ b → Codisjoint a b
Defined in
Mathlib.Order.Atoms
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeSupOrderTop
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Around this declaration

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

Ideal.isCoprime_of_isMaximal · cited by 3Ideal.isCoprime_of_isMaxi…IsCoatom.sup_eq_top_of_ne · cited by 0IsCoatom.sup_eq_top_of_neSemilatticeSup · cited by 785SemilatticeSupOrderTop · cited by 493OrderTopCodisjoint · cited by 197CodisjointIsCoatom · cited by 114IsCoatomIsCoatom.le_iff · cited by 4IsCoatom.le_iffIsCoatom.ne_top · cited by 2IsCoatom.ne_topIsCoatom.not_le_iff_codisjoint · cited by 2IsCoatom.not_le_iff_codis…IsCoatom.codisjoint_of_neCITED 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.