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Proof step 34 from proof inv-write_inode (previous step)

(ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)) = mkfile(m4, md3, m8, content1), dirs[ino] = mkdir(m9, md4, m10, m11, entries0), dirs[m] = mkdir(m5, md1, m6, m7, entries), files[m] = mkfile(m3, md0, # links(m, dirs), content), files[ino] = mkfile(m0, md2, m1, content0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries0 = ∅, ino ∈ dirs → m10 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m9 = # entries0 ∧ m11 = # subdirs(ino, dirs) ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m8 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content1 → # content1[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%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws) Used formulas: ino = m