Theorems · Theorem · order theory
lt_trans
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a < b → b < c → a < c- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 165 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.
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_leproof · cited by 438
Cited by165
Results whose statement or proof uses this declaration.
- LT.lt.transproof · cited by 370
- Real.log_posproof · cited by 51
- lt_asymmproof · cited by 16
- Real.rpow_lt_rpowproof · cited by 12
- Real.log_lt_logproof · cited by 10
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- Matrix.charpoly_monicproof · cited by 9
- AkraBazziRecurrence.differentiableAt_smoothingFnproof · cited by 8
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
- Real.rpow_lt_rpow_of_exponent_ltproof · cited by 5
- ONote.fundamentalSequence_has_propproof · cited by 5
- Real.summable_ofDigitsTermproof · cited by 5