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Proof step 12 from proof absexpt-pebs-write (previous step)

# vols[v0] = # avols[v0], vols[v][m] = ⌜n⌝ , apebs[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m2, boolvar), avols[v0][m0] = mapped(apebs[n, apeb][vols[v0][m0].pnum].data, m1), m < # vols[v], m0 < # avols[v0], valid-ebatbl(apebs, wlar, vols, n0), v ∈ vols, v0 ∈ vols, v0 ∈ avols, apebs[n, apeb][vols[v0][m0].pnum].fill ≤ m1, v0 ≠ v ∨ m0 ≠ m ⊦ vols[v0][m0] = unmapped, apebs[n, apeb][vols[v0][m0].pnum].data = buf ∧ m2 ≤ m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# vols[v0] = # avols[v0], avols[v0][m0] = mapped(buf0, m1), apebs[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m2, boolvar), vols[v][m] = ⌜n⌝ , apebs[n, apeb][vols[v0][m0].pnum] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), m0 < # avols[v0], m < # vols[v], valid-ebatbl(apebs, wlar, vols, n0), v0 ∈ avols, v0 ∈ vols, v ∈ vols, m3 ≤ m1, v0 ≠ v ∨ m0 ≠ m ⊦ vols[v0][m0] = unmapped, buf0 = buf ∧ m2 ≤ m1

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[n, apeb][vols[v0][m0].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[n, apeb][vols[v0][m0].pnum], aehdr0, avhdr0, buf0, m3, boolvar0