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Proof step 519 from proof inv-rename-file-dentry (previous step)

icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] = mkientry(boolvar0, mkinode(m2, md, boolvar, m5, m6, m7)), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], asynced2 → synced(files, icache0, pcache), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files ∧ icache0[ino0].inode.nlink = files[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files[icache0[ino0].inode.ino].meta, false, files[icache0[ino0].inode.ino].nlink, 0, files[icache0[ino0].inode.ino].size) ) ), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m5 = (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md, boolvar, m5, m6, m7) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).meta, true, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nlink, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nsubdirs, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).size) ;mkinode (ino, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).meta, false, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink, 0, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).size) ) )

Heuristic use patterns applied rule all left

And obtained the following new goals

Proof step 520:
dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ] [ino ] = mkientry(boolvar0, mkinode(m2, md, boolvar, m5, m6, m7)), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(dirs0, icache0, pcache), ino ∈ icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → 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) ) ), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files ∧ icache0[ino0].inode.nlink = files[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files[icache0[ino0].inode.ino].meta, false, files[icache0[ino0].inode.ino].nlink, 0, files[icache0[ino0].inode.ino].size) ) ), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, m2 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m5 = (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink ∧ m6 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md, boolvar, m5, m6, m7) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).meta, true, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nlink, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).nsubdirs, (ino = m3 ⊃ mkdir(m1, md2, # links(m3, dirs0), m4, entries);dirs0[ino]).size) ;mkinode (ino, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).meta, false, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).nlink, 0, (ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[ino]).size) ) )

Rule argument

pos: left 12 terms: ino abort: T discard: F computed: F

Additional information

Used terms: ino