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Proof step 48 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, # links(entries0[str], dirs0), content0), dirs = dirs0[m, mkdir(m0 - 1, md2, # links(m, dirs0), m4, entries0 -- str)], files = files0[entries0[str], mkfile(m1, md1, m2, content0)], afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, 1 ≤ m0, 1 ≤ # links(entries0[str], dirs0), asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m4, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, mkdentry(str, entries0[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))), # links(entries0[str], dirs0) = 0, m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# 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, md2, # links(m, dirs0), m4, entries0 -- str)], files = files0[entries0[str], mkfile(m1, md1, m2, content0)], m0 ≠ 0, afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, 1 ≤ m0, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m4, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, mkdentry(str, entries0[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base