Theorems · Theorem · order theory
LT.lt.trans
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a < b → b < c → a < cAlias of lt_trans.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 370 results in Mathlib
- Foundations
- Depth 7 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.
Cited by372
Results whose statement or proof uses this declaration.
- Ordinal.isNormal_opowproof · cited by 37
- Set.Ioo_eq_emptyproof · cited by 24
- Set.nonempty_Iooproof · cited by 23
- inv_lt_one_of_one_lt₀proof · cited by 20
- Complex.ne_zero_of_one_lt_reproof · cited by 18
- inv_strictAnti₀proof · cited by 10
- ContDiffBump.rOut_posproof · cited by 9
- NormedSpace.isVonNBounded_iffproof · cited by 9
- zpow_right_strictMono₀proof · cited by 8
- Fin.strictMono_succAboveproof · cited by 8
- Nat.le_log_of_pow_leproof · cited by 8
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
Showing the 200 most cited of 372.