Mathlib Map

Theorems · Theorem · order theory

le_imp_le_of_lt_imp_lt

∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : LinearOrder β] {a b : α} {c d : β},
  (d < c → b < a) → a ≤ b → c ≤ d
Defined in
Mathlib.Order.Defs.LinearOrder
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
PreorderLinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

le_imp_le_iff_lt_imp_lt · cited by 3le_imp_le_iff_lt_imp_ltnsmul_nonneg_iff · cited by 2nsmul_nonneg_iffone_le_pow_iff · cited by 2one_le_pow_iffLinearOrder · cited by 8572LinearOrderPreorder · cited by 7952Preorderle_of_not_gt · cited by 430le_of_not_gtnot_le_of_gt · cited by 97not_le_of_gtle_imp_le_of_lt_imp_ltCITED BYCITES

Cites4

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

Cited by3

Results whose statement or proof uses this declaration.