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Proof step 195 from proof inv-mkdir (previous step)

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 ] = mkientry(boolvar0, 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), 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), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files ∧ icache0[ino1].inode.nlink = files[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files[icache0[ino1].inode.ino].meta, false, files[icache0[ino1].inode.ino].nlink, 0, files[icache0[ino1].inode.ino].size) ) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0, m = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m2, m4) = (ino = ino0 ∨ ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .meta, true, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nlink, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nsubdirs, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic use patterns applied rule all left

And obtained the following new goals

Proof step 196:
dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, 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 ] = mkientry(boolvar0, mkinode(m, md0, boolvar, m1, m2, m4)), 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), 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), ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ icache0[ino].inode.ino ∈ files ∧ icache0[ino].inode.nlink = files[icache0[ino].inode.ino].nlink ∧ icache0[ino].inode.nsubdirs = 0 ∧ ¬ icache0[ino].inode.directory ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[ino].inode = (icache0[ino].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino].inode.ino, dirs0[icache0[ino].inode.ino].meta, true, dirs0[icache0[ino].inode.ino].nlink, dirs0[icache0[ino].inode.ino].nsubdirs, dirs0[icache0[ino].inode.ino].size) ;mkinode (icache0[ino].inode.ino, files[icache0[ino].inode.ino].meta, false, files[icache0[ino].inode.ino].nlink, 0, files[icache0[ino].inode.ino].size) ) ), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files ∧ icache0[ino1].inode.nlink = files[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files[icache0[ino1].inode.ino].meta, false, files[icache0[ino1].inode.ino].nlink, 0, files[icache0[ino1].inode.ino].size) ) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0, m = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino = ino0 ∨ ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m2, m4) = (ino = ino0 ∨ ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .meta, true, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nlink, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .nsubdirs, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ;(ino = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino]) ) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

pos: left 9 terms: ino abort: T discard: F computed: F

Additional information

Used terms: ino