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Proof step 188 from proof inv-mkdir (previous step)

dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), 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(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ], m0 ∈ dirs0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0, icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino ∧ (icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .dirty ⊃ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ∈ files ∧ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .nlink = files [icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] .nlink ∧ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .nsubdirs = 0 ∧ ¬ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .directory ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode = ( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ∨ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ∈ dirs0 ⊃ mkinode (icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino, ( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 )[icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] ) ) .meta, true, ( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 )[icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] ) ) .nlink, ( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 )[icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] ) ) .nsubdirs, ( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;( icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 )[icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] ) ) .size) ;mkinode (icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino, files [icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] .meta, false, files [icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] .nlink, 0, files [icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode .ino ] .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 189:
icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode = mkinode(m, md0, boolvar, m1, m2, m4), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), 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(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), afs-cons(dirs0, files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ], asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0, m = ino ∧ (icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .dirty ⊃ m ∈ files ∧ m1 = files[m].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode = (m = ino0 ∨ m ∈ dirs0 ⊃ mkinode (m, (m = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]) ) .meta, true, (m = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]) ) .nlink, (m = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]) ) .nsubdirs, (m = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]) ) .size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) )

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] → [icache0 [m0, mkientry (false, mkinode (m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode, m, md0, 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: icache0 [m0, mkientry (false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1)) ] [ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0)) ] [ino ] .inode, m, md0, boolvar, m1, m2, m4