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Proof step 28 from proof absexpt-idset (previous step)

# vols[v0] = # avols[v0], # apebs1 = # apebs0, wlar[n].status = used, vols[avhdr0.vol][avhdr0.leb] = ⌜n⌝ , apebs1[n] = mkpeb(aehdr, avhdr, buf, m1, boolvar), avols[v0][m0] = mapped(buf0, m2), vols[v0][m0] = ⌜n⌝ , apebs0[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), avhdr0.valid?, m0 < # avols[v0], n < # wlar, avhdr0.leb < # vols[avhdr0.vol], n < # apebs0, avhdr0.vol ∈ vols, v0 ∈ avols, v0 ∈ vols, m3 ≤ m2, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs0 ∧ n < # wlar ∧ apebs0[n].vidhdr.valid? ∧ apebs0[n].vidhdr.vol = v ∧ apebs0[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ avhdr0.vol ∨ m0 ≠ avhdr0.leb ⊦ n = n0, buf0 = buf ∧ m1 ≤ m2

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
# apebs1 = # apebs0, # vols[v0] = # avols[v0], wlar[n].status = used, apebs0[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), vols[v0][m0] = ⌜n⌝ , avols[v0][m0] = mapped(buf0, m2), apebs1[n] = mkpeb(aehdr, avhdr, buf, m1, boolvar), vols[v1][m4] = ⌜n⌝ , avhdr0 = avidhdr(v1, m4, m5, m6, m7), avhdr0.valid?, n < # apebs0, m4 < # vols[v1], n < # wlar, m0 < # avols[v0], v0 ∈ vols, v0 ∈ avols, v1 ∈ vols, m3 ≤ m2, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs0 ∧ n < # wlar ∧ apebs0[n].vidhdr.valid? ∧ apebs0[n].vidhdr.vol = v ∧ apebs0[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ v1 ∨ m0 ≠ m4 ⊦ n = n0, buf0 = buf ∧ m1 ≤ m2

Rule argument

spec: avidheader name: elim seq: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)) subst: [avhdr, v, m, m0, m1, m2] → [avhdr0, v1, m4, m5, m6, m7]

Additional information

Used simplifier rules: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)); (elim) Used terms: avhdr0, v1, m4, m5, m6, m7