Theorems · Theorem · order theory
not_infIrred
∀ {α : Type u_2} [inst : SemilatticeInf α] {a : α}, ¬InfIrred a ↔ IsMax a ∨ ∃ b c, b ⊓ c = a ∧ a < b ∧ a < c- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
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Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- IsMaxstatement · cited by 372
- InfIrredstatement · cited by 27
- not_supIrredproof · cited by 2
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