Theorems · Theorem · order theory
lt_imp_lt_of_le_imp_le
∀ {α : Type u_2} {β : Type u_5} [inst : LinearOrder α] [inst_1 : Preorder β] {a b : α} {c d : β},
(a ≤ b → c ≤ d) → d < c → b < a- Defined in
- Mathlib.Order.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- LinearOrderPreorder
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.
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- lt_of_not_geproof · cited by 374
- LE.le.not_gtproof · cited by 189
Cited by18
Results whose statement or proof uses this declaration.
- Real.rpow_lt_rpow_iffproof · cited by 9
- Real.rpow_lt_rpow_iff_of_negproof · cited by 5
- Nat.log_lt_of_lt_powproof · cited by 4
- Nat.lt_pow_of_log_ltproof · cited by 3
- Odd.pow_neg_iffproof · cited by 3
- pos_and_pos_or_neg_and_neg_of_mul_posproof · cited by 3
- le_imp_le_iff_lt_imp_ltproof · cited by 3
- Odd.zpow_neg_iffproof · cited by 3
- pos_and_pos_or_neg_and_neg_of_smul_posproof · cited by 2
- AddLECancellable.lt_tsub_iff_leftproof · cited by 1
- Ordinal.lt_log_of_lt_opowproof · cited by 1
- Cardinal.lt_cof_ord_powerproof · cited by 1