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Proof step 419 from proof inv-rename-dir-dentry (previous step)

dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs = dirs1[ino, dirs1[ino].meta:= inode.meta], dirs1 = dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)], ino = inode.ino, inode = mkinode(m, md2, true, # links(m, dirs0), m4, m1), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), ino ∈ dirs1, str0 ∈ entries0, entries0[str0] ∈ dirs0, m ∈ dirs0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3); dirs, files); new_child_inode := (mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino ∈ dirs ⊃ mkinode (mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino, dirs[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].meta, true, dirs[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].nlink, dirs[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].nsubdirs, dirs[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].size) ;mkinode (mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino, files[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].meta, false, files[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].nlink, 0, files[mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3).ino].size) ); old_parent_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) ); new_parent_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) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), entries0[str0] = ROOT_INO, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 420:
dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs = dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)], entries0[str0] ≠ ROOT_INO, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m ∈ dirs0, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(entries0[str0], md, true, # links(entries0[str0], dirs0), m6, m3); dirs, files); new_child_inode := (entries0[str0] ∈ dirs ⊃ mkinode(entries0[str0], dirs[entries0[str0]].meta, true, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, dirs[entries0[str0]].size) ;mkinode(entries0[str0], files[entries0[str0]].meta, false, files[entries0[str0]].nlink, 0, files[entries0[str0]].size) ); old_parent_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) ); new_parent_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) ); err := ESUCCESS; asynced := ?] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino).name, mkdentry(mkdentry(str0, entries0[str0]).name, mkdentry(str0, entries0[str0]).ino) ; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))))

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)