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Theorems · Theorem · order theory

Preorder.lt_iff_le_not_ge

∀ {α : Type u_2} [self : Preorder α] (a b : α), a < b ↔ a ≤ b ∧ ¬b ≤ a
Defined in
Mathlib.Order.Defs.PartialOrder
Cited by
1 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
Preorder

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Cites1

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

  • Preorderstatement and proof · cited by 7,952

Cited by2

Results whose statement or proof uses this declaration.