
Nonsymmetric Operads 97
an overlap. We call this overlap essential if lm(g
1
) and lm(g
2
) are the only
two divisors from lm(G) of the tree monomial obtained by merging these
monomials along their overlap.
Proposition 3.5.3.2 (Triangle lemma for nonsymmetric operads). Let G be
a self-reduced subset of T (X), and let g
1
, g
2
∈ G be two elements for which
lm(g
1
) and lm(g
2
) have an overlap. Suppose that this overlap is not essential,
so that there exists g
3
∈ G for which lm(g
3
) is another divisor of the tree
monomial T obtained by merging lm(g
1
) and lm(g
2
) along their overlap. Then:
• The divisors lm(g
1
) and lm(g
3
) of T have an overlap, and the divisors
lm(g