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Proof step 25 from proof abs-id-apebs-used (previous step)

# vols[v] = # avols[v], # wlar = # apebs, apebs[n, apeb][vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), wlar[n] = wl-entry(m0, stat), m < # avols[v], n < # apebs, valid-ebatbl(apebs, wlar, vols, n0), v ∈ avols, v ∈ vols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ stat = used, (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = buf ∧ m1 ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q)

User applied rule all left

And obtained the following new goals

Proof step 26:
# wlar = # apebs, # vols[v] = # avols[v], wlar[n] = wl-entry(m0, stat), apebs[n, apeb][vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), n < # apebs, m < # avols[v], valid-ebatbl(apebs, wlar, vols, n0), v ∈ vols, v ∈ avols, m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ stat = used, (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = buf ∧ m1 ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q)

Rule argument

pos: left 10 terms: m abort: F discard: T computed: T

Additional information

Used terms: m