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Proof step 76 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, asynced ↔ false, dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), err = ESUCCESS, inode = getinode (entries0[str], dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= m3).meta:= md0]), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode); icache_set# ((m0 ∈ dirs0 ⊃ mkinode(m0, md3, true, # links(m0, dirs0), m7, m8) ;mkinode (m0, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .meta, false, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .nlink, 0, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .size) ), false ; err, icache); dcache_delete#(m0, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons (dcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons (pcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache)))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 77:
# links(entries0[str], dirs0) = m2 + 1, asynced ↔ false, files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), err = ESUCCESS, icache = icache0[inode.ino, mkientry(asynced, inode)], inode = getinode (entries0[str], dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= m3).meta:= md0]), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, asynced1 → synced(files0, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪icache_set# ((m0 ∈ dirs0 ⊃ mkinode(m0, md3, true, # links(m0, dirs0), m7, m8) ;mkinode (m0, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .meta, false, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .nlink, 0, (m0 = entries0[str] ∧ entries0[str] ∈ files0 ⊃ (files0[entries0[str], mkfile(m1, md1, m2, content0)][entries0[str]].size:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).size) .meta:= mkinode(entries0[str], md0, false, m2 + 1, 0, m3).meta ;files0[entries0[str], mkfile(m1, md1, m2, content0)][m0] ) .size) ), false ; err, icache); dcache_delete#(m0, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ dcache-cons (dcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ pcache-cons (pcache, dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]) ∧ synced(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], icache, pcache) ∧ (asynced1 → synced(files0[entries0[str], mkfile(m3, md0, m2, content0)], icache, pcache)))

Proof step 76 from proof inv-unlink (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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