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Proof step 390 from proof inv-rename-file-dentry (previous step)

asynced ↔ false, files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), err = ESUCCESS, inode = mkinode(m, md2, true, # links(m, dirs0), m4, m1), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries[str0] ∈ files, str0 ∈ entries, m ∈ dirs0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); icache_set# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .meta, false, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .nlink, 0, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .size) ), false ; err, icache); inode := mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2); ino := entries[str0]; dirs := dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)]; icache_set# ((entries[str0] ∈ dirs ⊃ mkinode(entries[str0], dirs[entries[str0]].meta, true, dirs[entries[str0]].nlink, dirs[entries[str0]].nsubdirs, dirs[entries[str0]].size) ;mkinode (entries[str0], files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].meta, false, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].nlink, 0, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].size) ), false ; err, icache); dcache_delete# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), entries[str0] ∈ dirs0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 391:
asynced ↔ false, dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], inode = mkinode(m, md2, true, # links(m, dirs0), m4, m1), afs-cons(dirs0, files), afs-cons (dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)], files[entries[str0], mkfile(m2, md, # links(entries[str0], dirs0), content)]), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# ((m ∈ dirs0 ⊃ mkinode(m, md2, true, # links(m, dirs0), m4, m1) ;mkinode (m, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .meta, false, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .nlink, 0, files [entries[str0], files[entries[str0], files[entries[str0]].size:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).size] [entries[str0] ] .meta:= mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2).meta ] [m ] .size) ), false ; err, icache); inode := mkinode(entries[str0], md, false, # links(entries[str0], dirs0), 0, m2); ino := entries[str0]; dirs := dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries)]; icache_set# ((entries[str0] ∈ dirs ⊃ mkinode(entries[str0], dirs[entries[str0]].meta, true, dirs[entries[str0]].nlink, dirs[entries[str0]].nsubdirs, dirs[entries[str0]].size) ;mkinode (entries[str0], files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].meta, false, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].nlink, 0, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta][entries[str0]].size) ), false ; err, icache); dcache_delete# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(str0, entries[str0]).name ; err, dcache); dcache_set# ((m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).meta, false, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).nlink, 0, (m = ino ∧ ino ∈ files ⊃ (files[ino].size:= inode.size).meta:= inode.meta;files[m]).size) ) .ino, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries[str0]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons(icache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta]) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files[ino, (ino ∈ files ⊃ files[ino].size:= inode.size;files[ino]).meta:= inode.meta], icache, pcache))), entries[str0] ∈ dirs0

Proof step 390 from proof inv-rename-file-dentry (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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