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Proof step 9 from proof lf-mapped-valid-peb (previous step)

apebs[n].echdr = aechdr(m0), apebs[n].vidhdr.sqn = valid-sqns(v0, m1, apebs).max, wlar[n] = wl-entry(m0, used), vols[v][m] = ⌜n⌝ , m < # vols[v], n < # wlar, valid-ebatbl(apebs, wlar, vols, n0), valid-peb(v0, m1, apebs[n]), v ∈ vols ⊦ n = n0, apebs[n].bad, v0 = v ∧ m1 = m

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
avhdr.sqn = valid-sqns(v0, m1, apebs).max, vols[v][m] = ⌜n⌝ , wlar[n] = wl-entry(m0, used), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), aehdr = aechdr(m0), ¬ boolvar, n < # wlar, m < # vols[v], valid-ebatbl(apebs, wlar, vols, n0), valid-peb(v0, m1, apebs[n]), v ∈ vols ⊦ n = n0, v0 = v ∧ m1 = m

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], aehdr, avhdr, buf, m2, boolvar]

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], aehdr, avhdr, buf, m2, boolvar