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Proof step 528 from proof inv-write (previous step)

files[m] = mkfile(m2, md0, # links(m, dirs), content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), m ∈ files, fd ∈ of, m ∈ files0, n ≤ # buf0 ⊦ ino4 = 0, n = 0, of-cons(of[fd, mkfile(m, mode, m0 + ino4)], dirs, files[m, mkfile(m0 + ino4, md, # links(m, dirs), content)]), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err1 = ESUCCESS ∧ ¬ isdir

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 529:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 530:
files[m] = mkfile(m2, md0, # links(m, dirs), content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), n0 ∈ of[fd, mkfile(m, mode, m0 + ino4)], m ∈ files, fd ∈ of, m ∈ files0, n0 ∈ of, of[n0].ino ∈ files0, n ≤ # buf0 ⊦ ino4 = 0, n = 0, of[fd, mkfile(m, mode, m0 + ino4)][n0].ino ∈ files, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err1 = ESUCCESS ∧ ¬ isdir

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ fd = fd0 → of[fd0, file][fd] = file; (s)% ⊦ fd ∈ of[fd0, file] ↔ fd = fd0 ∨ fd ∈ of; (ws)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)