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Proof step 39 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;mkfile(m0, md, m3, content) ) = mkfile(m4, md0, m5, content1), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[ino] = mkfile(m0, md, m3, content), files0[m] = mkfile(m1, md1, # links(m, dirs), content0), dirs[ino] = mkdir(m6, md2, m7, m8, entries), ino = m, buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, ROOT_INO ∈ dirs, m2 ≤ n, ino ∈ dirs → m7 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0 ⊦ m2 % VFS_PAGE_SIZE = 0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files0 ∧ n1 ∈ content1 → # content1[n1] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, dirs[m] = mkdir(m6, md2, m7, m8, entries), files0[m] = mkfile(m0, md, # links(m, dirs), content0), buf-opt.some?, n1 * VFS_PAGE_SIZE < m2, n1 * VFS_PAGE_SIZE < n, afs-cons(dirs, files0), m ∈ files0, ROOT_INO ∈ dirs, n1 ∈ content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)], m2 ≤ n ⊦ # content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)][n1] = VFS_PAGE_SIZE, m2 % VFS_PAGE_SIZE = 0, m ∈ dirs

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (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) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)