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Proof step 394 from proof inv-rename-dir-dentry (previous step)

asynced0 ↔ old_ino = new_ino ∧ new_dent = old_dent, asynced1 ↔ new_dent.dentry?, dirs0[entries[str0]] = mkdir(m4, md3, # links(entries[str0], dirs0), m7, entries2), dirs0[entries1[str]] = mkdir(m1, md6, # links(entries1[str], dirs0), m3, ∅), dirs0[m] = mkdir(m2, md7, # links(m, dirs0), m5, entries1), dirs0[m0] = mkdir(m6, md4, # links(m0, dirs0), m9, entries), asynced0, asynced1, dirs = dirs1[new_ino, dirs1[new_ino].entries:= dirs1[new_ino].entries[new_dent.name, old_dent.ino]], dirs1 = dirs0[old_ino, dirs0[old_ino].entries:= (dirs0[old_ino].entries -- old_dent.name)], new_child_inode = mkinode(entries1[str], md, true, # links(entries1[str], dirs0), m3, m1), new_dent = mkdentry(str, entries1[str]), new_ino = new_parent_inode.ino, new_parent_inode = mkinode(m, md1, true, # links(m, dirs0), m5, m2), old_child_inode = mkinode(entries[str0], md0, true, # links(entries[str0], dirs0), m7, m4), old_dent = mkdentry(str0, entries[str0]), old_ino = old_parent_inode.ino, old_parent_inode = mkinode(m0, md2, true, # links(m0, dirs0), m9, m6), old_dent.dentry?, afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs0, files), synced(dirs0, icache, pcache), str0 ∈ entries, entries1[str] ∈ dirs0, entries[str0] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, str ∈ entries1, asynced2 → synced(files, icache, pcache), m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); 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, negdentry(old_dent.name).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(new_dent.name, old_dent.ino).name, mkdentry(new_dent.name, old_dent.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)))), entries1[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 395:
# links(entries[str0], dirs0) = dirs0[entries[str0]].nlink, # links(m, dirs0) = dirs0[m].nlink, dirs0[entries[str0]].entries = ∅, dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[m] = mkdir(dirs0[m].size, md7, dirs0[m].nlink, dirs0[m].nsubdirs, entries1), dirs0[entries[str0]] = mkdir(dirs0[entries[str0]].size, md6, dirs0[entries[str0]].nlink, dirs0[entries[str0]].nsubdirs, ∅), dirs0[entries[str0]] = mkdir(dirs0[entries[str0]].size, md3, dirs0[entries[str0]].nlink, dirs0[entries[str0]].nsubdirs, entries2), entries1[str0] = entries[str0], entries[str0] = dirs0[m].entries[str0], dirs = dirs0[m, dirs0[m].entries:= (dirs0[m].entries -- str0).entries:= dirs0[m].entries], entries[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), str0 ∈ entries1, m ∈ dirs0, entries[str0] ∈ dirs0, str0 ∈ entries, str0 ∈ dirs0[m].entries, asynced2 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md2, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(m, md2, true, # links(m, dirs0), dirs0[m].nsubdirs, dirs0[m].size); dirs, files); new_child_inode := mkinode(entries1[str0], md, true, # links(entries1[str0], dirs0), dirs0[entries1[str0]].nsubdirs, dirs0[entries1[str0]].size); afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := (new_child_inode.ino ∈ dirs ⊃ mkinode (new_child_inode.ino, dirs[new_child_inode.ino].meta, true, dirs[new_child_inode.ino].nlink, dirs[new_child_inode.ino].nsubdirs, dirs[new_child_inode.ino].size) ;mkinode(new_child_inode.ino, files[new_child_inode.ino].meta, false, files[new_child_inode.ino].nlink, 0, files[new_child_inode.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, entries[str0]).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str0, entries1[str0]).name, mkdentry(str0, entries[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: ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ entries[str] = ino ∧ str ∈ entries → entries[str, ino] = entries; (s)% ⊦ (entries -- str)[str, ino] = entries[str, ino]; (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ negdentry(str).name = str; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ ¬ mkdentry(str, m).negdentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)% ⊦ mkdentry(str, m) = mkdentry(str0, m0) ↔ str = str0 ∧ m = m0; (ws)% ⊦ (ad.entries:= entries).entries = entries; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)