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Proof step 376 from proof inv-write (previous step)

(ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0 upto m1);mkfile(m2, md0, m3, content)) = mkfile(m4, md1, m5, content1), dirs[ino] = mkdir(m6, md2, m7, m8, entries), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files0[ino] = mkfile(m2, md0, m3, content), dom of < ino3, afs-cons(dirs, files0), of-cons(of, dirs, files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)]), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs → m7 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs) ⊦ n0 = 0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files0 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

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)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%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% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s) Used formulas: ino = m