Theorems · Theorem · order theory
gt_trans
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, b < a → c < b → c < a- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- le_of_ltproof · cited by 1,175
- lt_of_lt_of_le'proof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- LT.lt.trans'proof · cited by 15
- List.not_lt_of_mem_argminproof · cited by 2
- WithTop.lt_iff_exists_coe_btwn'proof · cited by 1
- lt_trans'proof · cited by 0