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Proof step 43 from proof valid-ebatbl-unmap (previous step)

wlar[n].status = used, apebs[n].vidhdr = avidhdr(v0, m0, m6, m7, m8), vols[v0][m0] = ⌜n⌝ , apebs[n1] = mkpeb(aehdr, avidhdr(v0, m0, m1, m4, m5), buf, m3, boolvar), wlar[n1] = wl-entry(m2, used), m0 < # vols[v0], n < # wlar, n < # apebs, n1 < # apebs, n1 < # wlar, v0 ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ n = n0, n1 = n, n1 = n0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
wlar[n].status = used, wlar[n1] = wl-entry(m2, used), apebs[n1] = mkpeb(aehdr, avidhdr(v0, m0, m1, m4, m5), buf, m3, boolvar), vols[v0][m0] = ⌜n⌝ , apebs[n] = mkpeb(aehdr0, avhdr, buf0, m9, boolvar0), avhdr = avidhdr(v0, m0, m6, m7, m8), n1 < # wlar, n1 < # apebs, n < # apebs, n < # wlar, m0 < # vols[v0], v0 ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ n = n0, n1 = n0, n1 = n

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], aehdr0, avhdr, buf0, m9, 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], aehdr0, avhdr, buf0, m9, boolvar0