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Theorems · Theorem · order theory

Ne.lt_sup_or_lt_sup

∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a ≠ b → a < a ⊔ b ∨ b < a ⊔ b
Defined in
Mathlib.Order.Lattice
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeSup
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Around this declaration

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

WCovBy.sup_eq · cited by 0WCovBy.sup_eqSemilatticeSup · cited by 785SemilatticeSupleft_lt_sup · cited by 7left_lt_supright_lt_sup · cited by 6right_lt_supNe.not_le_or_not_ge · cited by 3Ne.not_le_or_not_geNe.lt_sup_or_lt_supCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.