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Proof step 61 from proof inv-mkdir (previous step)

(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0] = mkdir(m, md0, m1, m2, entries), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), err = ESUCCESS, ino0 ≠ 0, afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files, ¬ str ∈ entries0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ dcache-cons (dcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ pcache-cons (pcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ synced ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache) ∧ ( asynced1 → synced (files, icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 62:
dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0] = mkdir(m, md0, m1, m2, entries), dent = mkdentry(str, ino0), err = ESUCCESS, name = str, p_ino = m0, afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪let key = dentrykey(p_ino, name) in dcache[key] := dent⟫ ( icache-cons (icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ dcache-cons (dcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ pcache-cons (pcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ synced ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache) ∧ ( asynced1 → synced (files, icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache))), ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0

Rule argument

pos: right 1

Additional information

Used simplifier rules: dcache_set#(P_INO, NAME, DENT; ERR, DCACHE) {let KEY = dentrykey(P_INO, NAME) in DCACHE[KEY] := DENT};