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Proof step 29 from proof abs-id-apebs-used (previous step)

# 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), avols[v][m] = mapped(apebs[vols[v][m].pnum].data, m2), n < # apebs, m < # avols[v], valid-ebatbl(apebs, wlar, vols, n0), v ∈ vols, v ∈ avols, apebs[vols[v][m].pnum].fill ≤ m2 ⊦ vols[v][m] = unmapped, stat = used, apebs[vols[v][m].pnum].data = buf ∧ m1 ≤ m2

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
# vols[v] = # avols[v], # wlar = # apebs, avols[v][m] = mapped(buf0, m2), apebs[n, apeb][vols[v][m].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), wlar[n] = wl-entry(m0, stat), apebs[vols[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), m < # avols[v], n < # apebs, valid-ebatbl(apebs, wlar, vols, n0), v ∈ avols, v ∈ vols, m3 ≤ m2 ⊦ vols[v][m] = unmapped, stat = used, buf0 = buf ∧ m1 ≤ m2

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[vols[v][m].pnum], aehdr0, avhdr0, buf0, m3, boolvar0]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[vols[v][m].pnum], aehdr0, avhdr0, buf0, m3, boolvar0