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Proof step 10 from proof absexpt-idset (previous step)

# vols[v0] = # avols[v0], vols[v][m] = ⌜n⌝ , apebs1[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), avols[v0][m0] = mapped(apebs0[vols[v0][m0].pnum].data, m2), m < # vols[v], m0 < # avols[v0], id(apebs1, apebs0, mapped-pebs(vols) -- n), valid-ebatbl(apebs0, wlar, vols, n0), v ∈ vols, v0 ∈ vols, v0 ∈ avols, apebs0[vols[v0][m0].pnum].fill ≤ m2, v0 ≠ v ∨ m0 ≠ m ⊦ vols[v0][m0] = unmapped, apebs0[vols[v0][m0].pnum].data = buf ∧ m1 ≤ m2

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
# vols[v0] = # avols[v0], avols[v0][m0] = mapped(buf0, m2), apebs1[vols[v0][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v][m] = ⌜n⌝ , apebs0[vols[v0][m0].pnum] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), m0 < # avols[v0], m < # vols[v], id(apebs1, apebs0, mapped-pebs(vols) -- n), valid-ebatbl(apebs0, wlar, vols, n0), v0 ∈ avols, v0 ∈ vols, v ∈ vols, m3 ≤ m2, v0 ≠ v ∨ m0 ≠ m ⊦ vols[v0][m0] = unmapped, 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] → [apebs0[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: apebs0[vols[v0][m0].pnum], aehdr0, avhdr0, buf0, m3, boolvar0