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Proof step 581 from proof inv-write (previous step)

of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), dirs1 = dirs, err = ESUCCESS, err0 = ESUCCESS, files1 = files0[m, mkfile(m1, md, # links(m, dirs), content0 upto m1)], ino = m1, ino0 = m0 + n, ino1 = m0 + ino4, ino2 = 0, ino4 = ino5, ino6 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir0, n0 = ino4, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, n ≤ # buf0 ⊦ ino4 = 0, n = 0, err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, ino4 ≠ 0 ∧ ino < ino1, of-cons(of[fd, of[fd].pos:= (m0 + n0)], dirs, files) ∧ dom of[fd, of[fd].pos:= (m0 + n0)] < ino3 ∧ afs-cons(dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 582:
⊦ 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 583:
of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, n0 ∈ of[fd, mkfile(m, mode, m0 + ino4)], n0 ∈ of, of[n0].ino ∈ files, n ≤ # buf0, m0 + ino4 ≤ m1 ⊦ ino4 = 0, n = 0, of[fd, mkfile(m, mode, m0 + ino4)][n0].ino ∈ files, err1 = ESUCCESS ∧ ¬ isdir, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

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)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)