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Proof step 52 from proof inv-mkdir (previous step)

(m ∈ dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) = mkinode(m0, md2, boolvar, m1, m2, m4), dirs0[m] = mkdir(m3, md1, # links(m, dirs0), m5, entries0), err = ESUCCESS, afs-cons ((dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, md0, true, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].nlink, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].nsubdirs, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].size), false ; err, icache); icache_set# (getinode (mkdentry(str, ino0).ino, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ dirs0[ino0, mkdir(m3 + 1, md1, # links(ino0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m] ) .meta:= md0 ], files), false ; err, icache); dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ dcache-cons (dcache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ pcache-cons (pcache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ synced ((dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), ino0 = 0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
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, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].meta:= md2 ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m0 ∈ dirs0, ¬ str ∈ entries0, ¬ ino0 ∈ files, ¬ ino0 ∈ dirs0, asynced1 → synced(files, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m0, md2, true, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].nlink, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].nsubdirs, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0].size), false ; err, icache); 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)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)