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Proof step 54 from proof afs-cons-rename-file-dentry (previous step)

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

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%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