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Proof step 41 from proof inv-fsync (previous step)

⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), isdir ↔ isdir0, files[ino0] = mkfile(m, md, # links(ino0, dirs), content), err = ESUCCESS, ino1 = ROOT_INO, inode = mkinode(ino0, md, false, # links(ino0, dirs), 0, m), afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, p, ROOT_INO, dirs, files), valid-file-inode(inode, dirs, files), ino0 ∈ files ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true, ino0 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
⟨vfs_walk#(p, user, dirs, files, asynced; ino1, err)⟩ (ino1 = ino0 ∧ err = ESUCCESS), # links(ino0, dirs) = files[ino0].nlink, files[ino0] = mkfile(m, md, files[ino0].nlink, content), err = ESUCCESS, ino1 = ROOT_INO, afs-cons(dirs, files), ispath(p, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, p, ROOT_INO, dirs, files), ino0 ∈ files, ¬ ino0 ∈ dirs ⊦ ⟪fail_or_success#(; ; err); choose bv with true in asynced := bv; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true

Rule argument

Additional information

Used simplifier rules: 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% ⊦ 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).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)