The consequences of the cosmological constant ansatz of Carvalho, Lima, and Waga (=3H2+3R-2) are investigated in an extension of the nonsingular zer-Taha cosmology. The considered model describes a closed singularity-free universe evolving through successive epochs of pure radiation, matter generation, and radiation and matter. The early phase of the last period is shown to be a concrete realization of the postsingularity radiation era scenario of Freese, Adams, Frieman, and Mottola. © 1994 The American Physical Society.