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Proof step 206 from proof refine-unlink (previous step)

isdir0 ↔ isdir2, isdir1 ↔ false, entries[str] ∈ dirs ↔ root[q + str '].dir?, isdir2 ↔ p_inode.directory, isdir ↔ false, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), err = ESUCCESS, err1 = err, err2 = ESUCCESS, ino = mkdentry(str, entries[str]).ino, inode = p_inode0, ¬ isdir2, p_inode = getinode(ino, dirs, files), mkdentry(str, entries[str]).dentry?, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md, true, # links(ino1, dirs), m1, # entries) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); dent := mkdentry(str, dirs[ino1].entries[str]); afs_unlink#(; inode, p_inode, dent, err1, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err1, dirs, files)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 207:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), err = ESUCCESS, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, entries[str] ∈ files, ¬ root[q + str '].dir?, ¬ entries[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_check_commit#(dirs, files; err; asynced); fs := abs-files(files); if err = ESUCCESS then {inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md, true, # links(ino1, dirs), m1, # entries) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ); dent := mkdentry(str, dirs[ino1].entries[str]); p_inode := getinode(mkdentry(str, entries[str]).ino, dirs, files); afs_unlink#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (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)% ⊦ mkdentry(str, m).ino = m; (s)