e/Honest leftmost branch

Information
has gloss	eng: In graph theory, an honest leftmost branch of a tree T on ω × γ is a branch ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). (Here, [T] denotes the set of branches of maximal length of T, ω the ordinal (represented by the natural numbers) N and γ some other ordinal.)
lexicalization	eng: Honest leftmost branch
instance of	e/Tree (set theory)