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Proof step 57 from proof inv-mkdir (previous step)

asynced ↔ false, 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), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], inode = mkinode(m0, md2, true, m1, m2, m), 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 ⊦ ⟪icache_set# (getinode (mkdentry(str, ino0).ino, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, (m0 = ino0 ∧ ino0 ∈ dirs0[ino0, mkdir(m3 + 1, md1, # links(ino0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0] ) .meta:= md2 ], files), false ; err, icache); dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].meta:= md2 ], 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, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].meta:= md2 ], 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, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].meta:= md2 ], files) ∧ synced ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].meta:= md2 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
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), err = ESUCCESS, icache = icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))], ino0 ≠ 0, 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, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files, ¬ str ∈ entries0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (getinode (mkdentry(str, ino0).ino, (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), false ; err, icache); dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache, (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) ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)