[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 597 from proof inv-write (previous step)

files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), 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 = 0, ino4 = ino5, ino6 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir0, n0 = ino4, dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n ≤ # buf0 ⊦ n = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, err = ESUCCESS ∧ ¬ isdir, 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 598:
⊦ 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 599:
files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n0 ∈ of, of[n0].ino ∈ files0, n ≤ # buf0 ⊦ n = 0, of[n0].ino ∈ files, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

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[fd] = file ∧ fd ∈ of → of[fd, file] = of; (s)% ⊦ 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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)