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Proof step 7 from proof valid-ebatbl-add-unmapped-vol (previous step)

wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2] = wl-entry(m4, stat), wlar[n1] = wl-entry(m2, free), apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), vols[v, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n2⌝ , m < # vols[v, fill(mkebatbl(n), unmapped)][v0], v0 ∈ vols[v, fill(mkebatbl(n), unmapped)], ∀ 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 ⊦ v ∈ vols, stat = used ∧ n2 < # apebs ∧ n2 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m ∧ n2 ≠ n1

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
vols[v, fill(mkebatbl(n), unmapped)][v0][m] = ⌜n2⌝ , apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), wlar[n1] = wl-entry(m2, free), wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2] = wl-entry(m4, stat), m < # vols[v, fill(mkebatbl(n), unmapped)][v0], v0 ∈ vols[v, fill(mkebatbl(n), unmapped)], ∀ 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 ⊦ v0 = v, v ∈ vols, stat = used ∧ n2 < # apebs ∧ n2 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m ∧ n2 ≠ n1

Rule argument

fma: v0 = v

Additional information

Used simplifier rules: ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)% ⊦ # fill(ebatbl, ebae) = # ebatbl; (s)% ⊦ # mkebatbl(n) = n; (s)% ⊦ m < n → fill(mkebatbl(n), ebae)[m] = ebae; (s)% ⊦ unmapped ≠ ⌜m⌝ ; (s) Used formulas: v0 = v