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Proof step 51 from proof inv-mkdir (previous step)

dirs0[m] = mkdir(m3, md1, # links(m, dirs0), m5, entries0), err = ESUCCESS, ino0 ≠ 0, afs-cons(dirs0, files), 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), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ str ∈ entries0, ¬ ino0 ∈ files, ¬ ino0 ∈ 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# ((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) ) .ino, 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)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [( 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) ), m0, md2, boolvar, m1, m2, m4]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: ( 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) ), m0, md2, boolvar, m1, m2, m4