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Proof step 31 from proof valid-ebatbl-add-unmapped-vol (previous step)

wlar[n1] = wl-entry(m2, free), apebs[n2] = mkpeb(aehdr, avidhdr(v0, m5, m6, m7, m8), buf, m3, boolvar), wlar[n2] = wl-entry(m4, used), n2 < # apebs, n2 < # wlar, ∀ 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 ⊦ n2 = n0, n2 = n1, v ∈ vols, vols[v, fill(mkebatbl(n), unmapped)][v0][m5] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m5 < # vols[v, fill(mkebatbl(n), unmapped)][v0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 32:
wlar[n2] = wl-entry(m4, used), apebs[n2] = mkpeb(aehdr, avidhdr(v0, m5, m6, m7, m8), buf, m3, boolvar), wlar[n1] = wl-entry(m2, free), v0 = v, n2 < # wlar, n2 < # apebs, ∀ 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 ⊦ n2 = n1, n2 = n0, v ∈ vols, vols[v, fill(mkebatbl(n), unmapped)][v0][m5] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m5 < # vols[v, fill(mkebatbl(n), unmapped)][v0]
Proof step 36:
wlar[n2] = wl-entry(m4, used), apebs[n2] = mkpeb(aehdr, avidhdr(v0, m5, m6, m7, m8), buf, m3, boolvar), wlar[n1] = wl-entry(m2, free), n2 < # wlar, n2 < # apebs, ∀ 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 ⊦ n2 = n1, n2 = n0, v0 = v, v ∈ vols, vols[v, fill(mkebatbl(n), unmapped)][v0][m5] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m5 < # vols[v, fill(mkebatbl(n), unmapped)][v0]

Rule argument

fma: v0 = v

Additional information

Used formulas: v0 = v