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Theorems · Theorem · order theory

le_imp_le_iff_lt_imp_lt

∀ {α : Type u_2} {β : Type u_5} [inst : LinearOrder α] [inst_1 : LinearOrder β] {a b : α} {c d : β},
  a ≤ b → c ≤ d ↔ d < c → b < a
Defined in
Mathlib.Order.Basic
Cited by
3 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
LinearOrderLinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Nat.floor_le_of_le · cited by 2Nat.floor_le_of_leArchimedeanClass.stdPart_le_of_le · cited by 1ArchimedeanClass.stdPart_…ArchimedeanClass.le_stdPart_of_le · cited by 1ArchimedeanClass.le_stdPa…LinearOrder · cited by 8572LinearOrderlt_imp_lt_of_le_imp_le · cited by 18lt_imp_lt_of_le_imp_lele_imp_le_of_lt_imp_lt · cited by 3le_imp_le_of_lt_imp_ltle_imp_le_iff_lt_imp_ltCITED BYCITES

Cites3

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Cited by3

Results whose statement or proof uses this declaration.