Mathlib Map

Theorems · Theorem · order theory

LE.le.trans_lt

∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b < c → a < c

Alias 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.

Cited by795

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 795.