Theorems · Theorem · order theory
LT.lt.trans_le
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a < b → b ≤ c → a < cAlias of lt_of_lt_of_le.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 678 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- lt_of_lt_of_leproof · cited by 438
Cited by678
Results whose statement or proof uses this declaration.
- zero_lt_twoproof · cited by 124
- lt_imp_lt_of_le_of_leproof · cited by 53
- ne_top_of_ltproof · cited by 50
- Real.log_le_logproof · cited by 39
- lt_max_of_lt_rightproof · cited by 29
- Real.log_nonnegproof · cited by 28
- inv_anti₀proof · cited by 27
- Set.Ioo_subset_Iooproof · cited by 19
- Nat.cast_add_one_posproof · cited by 18
- ContinuousLinearMap.isBoundedBilinearMapproof · cited by 18
- inv_le_one_of_one_le₀proof · cited by 16
- lt_max_of_lt_leftproof · cited by 16
Showing the 200 most cited of 678.