[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 568 from proof inv-write (previous step)

files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs1 = dirs, err = err0, err2 = ESUCCESS, dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n ≤ # buf0, (m0 ≤ m1 ⊃ m1 ≥ m0;true), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ err = ESUCCESS, ino4 = 0, n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err1 = ESUCCESS ∧ ¬ isdir, of-cons(of[fd, of[fd].pos:= (m0 + (m0 ≤ m1 ⊃ m1 - m0;0))], dirs, files) ∧ dom of[fd, of[fd].pos:= (m0 + (m0 ≤ m1 ⊃ m1 - m0;0))] < ino3 ∧ afs-cons(dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 569:
⊦ 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 570:
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), fd ∈ of, m ∈ files0, n0 ∈ of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))], n0 ∈ of, of[n0].ino ∈ files0, n ≤ # buf0, ⌊err0⌋ ⊦ ino4 = 0, n = 0, of[fd, mkfile(m, mode, m0 + (m0 ≤ m1 ⊃ m1 - m0;0))][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)% ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)