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Theorems · Theorem · order theory

lt_isLUB_iff

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {a b : α}, IsLUB s a → (b < a ↔ ∃ c ∈ s, b < c)
Defined in
Mathlib.Order.Bounds.Basic
Cited by
7 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder

Around this declaration

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

Cites4

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

  • Setstatement and proof · cited by 53,352
  • LinearOrderstatement and proof · cited by 8,572
  • IsLUBstatement and proof · cited by 280
  • isLUB_le_iffproof · cited by 24

Cited by7

Results whose statement or proof uses this declaration.