 Flasque-kernel section-lifting lemma

For a short exact sequence of sheaves with flasque sheaf kernel, every section of the quotient on any open set lifts to the middle sheaf on that set. Use the Zorn lemma to choose a maximal partial lift, with chains glued by the sheaf gluing axiom. A new local lift differs from the old one on their overlap by a kernel section. Extend that difference by flasqueness, adjust the new lift, and glue, contradicting maximality unless its domain is the entire open set. Consequently a quotient of two flasque sheaves is flasque. With an injective resolution of sheaves, the long exact sequence in sheaf cohomology and repeated dimension shifts prove that flasque sheaves have zero positive-degree cohomology.