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Proof step 9 from proof valid-ebatbl-update-vhdrs-unused (previous step)

vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[m, apeb][n0].vidhdr.valid? ∧ apebs[m, apeb][n0].vidhdr.vol = v ∧ apebs[m, apeb][n0].vidhdr.leb = m1 ∧ n0 ≠ n, wlar[n0] = wl-entry(m3, stat0), wlar[m] = wl-entry(m0, stat), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), ∀ v, m1, n0. vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ wlar[n0].status = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[m, apeb][n0].vidhdr.valid? ∧ apebs[m, apeb][n0].vidhdr.vol = v ∧ apebs[m, apeb][n0].vidhdr.leb = m1 ∧ n0 ≠ n ⊦ vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m1 ∧ n0 ≠ n, stat = used

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m1 ∧ n0 ≠ n, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[m] = wl-entry(m0, stat), wlar[n0] = wl-entry(m3, stat0), apebs[m, apeb][n0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), ∀ v, m1, n0. vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ wlar[n0].status = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[m, apeb][n0].vidhdr.valid? ∧ apebs[m, apeb][n0].vidhdr.vol = v ∧ apebs[m, apeb][n0].vidhdr.leb = m1 ∧ n0 ≠ n ⊦ vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m1 ∧ n0 ≠ n, stat = used

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[m, apeb][n0], aehdr0, avhdr0, buf0, m4, 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[m, apeb][n0], aehdr0, avhdr0, buf0, m4, boolvar0