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Proof step 12 from proof valid-ebatbl-write-data (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), ∀ 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 ⊦ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.valid? ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.vol = v ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.leb = m ∧ n1 ≠ n0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1] = mkpeb(aehdr0, avhdr0, buf, m2, boolvar0), ∀ 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 ⊦ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m ∧ n1 ≠ n0

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, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1], aehdr0, avhdr0, buf, 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: apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1], aehdr0, avhdr0, buf, m2, boolvar0