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Proof step 10 from proof abs-idset-fwd (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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