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Proof step 133 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] [m0, mkientry(false, mkinode(m0, md3, true, # links(m0, dirs0), m7, m8)) ] [ino ] = mkientry(true, inode0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), icache0[ino] = mkientry(boolvar0, inode), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, ino ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ino ∈ icache0 → ¬ boolvar0, datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, ino = m0 ∨ ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))] ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 134:
# links(entries0[str], dirs0) = m2 + 1, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))][ino] = mkientry(true, inode0), icache0[ino] = mkientry(false, inode), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), ino ∈ icache0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m2, 0, m3))], ino ∈ dirs0, m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, asynced1 → synced(files0, icache0, pcache), datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = m0

Rule argument

Additional information

Used simplifier rules: ⊦ ino = ino0 → icache[ino0, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ icache[ino, ie][ino] = ie; (s)