Let
E be a toric fibration arising from symplectic reduction of a direct sum of complex line bundles over (almost) K
ähler base
B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let
La be convex line bundles over
B,
Aa smooth divisors of
B arising as the zero loci of generic sections of
La , and
a particular fixed-point section of
E. Further assume the {
Aa} to be mutually disjoint. The manifold
is a new manifold with tautological line bundles over new projective spaces in the geometry, where previously there was a simpler vector bundle in the given local geometry (Section 1.5). Thus, we compute genus-0 Gromov-Witten invariants of
in terms of genus-0 Gromov-Witten invariants of
B and of
{Aa}, the matrix used for the symplectic reduction description of the fiber of the toric fibration
E→B, and the restriction maps
. The proofs utilize the fixed-point localization technique describing the geometry of
and its genus-0 Gromov-Witten theory, as well as the Quantum Lefschetz theorem relating the genus-0 Gromov-Witten theory of
A with that of
B.