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Proof step 206 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m4, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs = dirs0[m, mkdir(m0 - 1, md, # links(m, dirs0), m4, entries0 -- str)], files = files0[entries0[str], mkfile(m1, md1, m2, content0)], ino = inode.ino, inode = mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), ino ∈ dirs, str ∈ entries0, entries0[str] ∈ files0, m ∈ dirs0, 1 ≤ m0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [c_inode := getinode(entries0[str], dirs[ino, dirs[ino].meta:= inode.meta], files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), asynced ; err, icache); dcache_delete# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, mkdentry(str, entries0[str]).name ; err, dcache)}⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), m0 = 0, ino ∈ files

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)