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Theorem max-avol-at

⊦ n < # ebatbl → max-avol(apebs, ebatbl, v, q)[n] = (ebatbl[n] ≠ unmapped ⊃ mapped(apebs[ebatbl[n].pnum].data, apebs[ebatbl[n].pnum].fill);(v × n ∈ q ⊃ unmapped;erased))