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Proof step 14 from proof afs-cons-inode-sync (previous step)

(ino = m ⊃ (files[m].size:= m2).meta:= md;mkfile(m0, md0, m1, content)) = mkfile(m3, md1, m4, content0), dirs[ino] = mkdir(m5, md2, m6, m7, entries), files[ino] = mkfile(m0, md0, m1, content), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs → m6 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m5 = # entries ∧ m7 = # subdirs(ino, dirs) ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%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% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s) Used formulas: ino = m