Theorems · Theorem · order theory
LE.le.trans_lt
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b < c → a < cAlias of lt_of_le_of_lt.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 795 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_le_of_ltproof · cited by 432
Cited by795
Results whose statement or proof uses this declaration.
- ne_top_of_le_ne_topproof · cited by 68
- lt_imp_lt_of_le_of_leproof · cited by 53
- MeasureTheory.measure_lt_topproof · cited by 39
- add_lt_add_of_lt_of_leproof · cited by 37
- add_lt_add_of_le_of_ltproof · cited by 31
- Set.Ico_eq_emptyproof · cited by 24
- pos_of_gtproof · cited by 24
- Module.rank_lt_aleph0proof · cited by 23
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Set.Ioo_subset_Iooproof · cited by 19
- mul_lt_mul_of_lt_of_leproof · cited by 18
- Polynomial.derivative_mapproof · cited by 17
Showing the 200 most cited of 795.