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Proof step 91 from proof inv-rename-file-dentry (previous step)

(m = m0 ⊃ mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), asynced1 ↔ true, dirs0[m0] = mkdir(m1 + 1, md6, # links(m0, dirs0), m7, entries), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), files0[entries1[str]] = mkfile(m5, md5, # links(entries1[str], dirs0), content1), dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m8, entries1), dirs = dirs0[m0, mkdir(m1, md6, # links(m0, dirs0), m7, entries -- str0)][m, mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])], files = files0[ino, files0[ino].nlink:= (files0[ino].nlink - 1)], ino = mkdentry(str, entries1[str]).ino, old_dent = mkdentry(str0, entries[str0]), mkdentry(str, entries1[str]).dentry?, old_dent.dentry?, afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str0 ∈ entries, entries[str0] ∈ files0, entries1[str] ∈ files0, m0 ∈ dirs0, m ∈ dirs0, str ∈ entries1, files0[ino].nlink ≥ 1, m = m0 → md1 = md2, asynced2 → synced(files0, icache, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m0, md2, true, # links(m0, dirs0), m7, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m8, m4); dirs, files); new_child_inode := mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2); if asynced1 then {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 := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].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, negdentry(old_dent.name).name; err, dcache); dcache_set# (new_parent_inode.ino, mkdentry(mkdentry(str, entries1[str]).name, old_dent.ino).name, mkdentry(mkdentry(str, entries1[str]).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)))), entries[str0] ∈ dirs0, entries1[str] ∈ dirs0, m0 = m ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]% ⊦ mkfile(m, md, m0, content).nlink:= m2 = mkfile(m, md, m2, content); (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ negdentry(str).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkdentry(str, m).ino = m; (s)