Theorems · Theorem · order theory
ge_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
- 34 results in Mathlib
- Foundations
- Depth 4 from the axioms · 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.
Cited by34
Results whose statement or proof uses this declaration.
- LE.le.trans'proof · cited by 140
- le_inf_iffproof · cited by 48
- inf_le_of_left_leproof · cited by 17
- lt_of_lt_of_le'proof · cited by 15
- lt_of_le_of_lt'proof · cited by 11
- inf_le_of_right_leproof · cited by 10
- csInf_le_of_leproof · cited by 6
- isUpperSet_Iciproof · cited by 5
- Subgroup.normal_le_normalCoreproof · cited by 5
- max_assocproof · cited by 5
- AddSubgroup.normal_le_normalCoreproof · cited by 4
- Filter.tendsto_atBot_atBot_of_monotoneproof · cited by 3