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Proof step 93 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, (ino = m ⊃ mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1) ;mkfile(m2, md0, m3, content) ) = mkfile(m4, md1, m5, content1), files1[ino] = mkfile(m2, md0, m3, content), files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs[ino] = mkdir(m6, md2, m7, m8, entries), ino = m, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[m, mkfile(m1, md, # links(m, dirs), content0[m1 / VFS_PAGE_SIZE, fill(content0[m1 / VFS_PAGE_SIZE], zero, n2, n1)] upto m1)]), ROOT_INO ∈ dirs, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino ∈ dirs → m7 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs), ino ∈ files1 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files1 ⊦ n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, (ino ∈ files1 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files1 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 94:
m4 + n1 = m4 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m4, md, # links(m, dirs), content0), dirs[m] = mkdir(m6, md2, m7, m8, entries), of[fd] = mkfile(m, mode, m0), m4 = n2 + m4 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n * VFS_PAGE_SIZE < m4, dom of < ino3, afs-cons(dirs, files1), of-cons (of, dirs, files1[m, mkfile(m4, md, # links(m, dirs), content0[m4 / VFS_PAGE_SIZE, fill(content0[m4 / VFS_PAGE_SIZE], zero, n2, n1)] upto m4)]), of-cons(of, dirs, files1), n ∈ content0[m4 / VFS_PAGE_SIZE, fill(content0[m4 / VFS_PAGE_SIZE], zero, n2, n1)], m ∈ files1, m4 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, ROOT_INO ∈ dirs, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ # content0[m4 / VFS_PAGE_SIZE, fill(content0[m4 / VFS_PAGE_SIZE], zero, n2, n1)][n] = VFS_PAGE_SIZE, n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%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%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)