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

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Proof step 419 from proof inv-write (previous step)

VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files[m] = mkfile(m2, md0, # links(m, dirs), content), 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), of-cons (of, dirs, files [m, mkfile (m2, md0, # links(m, dirs), content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1))]) ]), m ∈ files0, fd ∈ of, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, m ∈ files, ino0 ≤ # buf0, n0 ≤ # buf0, ino0 ≤ n0, ino0 + min(n0 - ino0, n1) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n1) ≤ VFS_PAGE_SIZE ⊦ min(n0 - ino0, n1) = 0, n0 = 0, afs-cons (dirs, files [m, mkfile (m2, md0, # links(m, dirs), content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1))]) ]), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 420:
⊦ afs-cons(dirs0, files0) → ( afs-cons(dirs1, files1) ↔ (∀ ino, name, n. ROOT_INO ∈ dirs0 ∧ (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files0)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files0 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino(dirs0[ino].entries[name], dirs0, files0)) ∧ (ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) → ROOT_INO ∈ dirs1 ∧ (ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dir-empty(ino, dirs1, files1)) ∧ ( ino ∈ dirs1 → ¬ ino ∈ files1 ∧ dirs1[ino].nlink = # links(ino, dirs1) ∧ dirs1[ino].nlink ≤ 1 ∧ dirs1[ino].size = # dirs1[ino].entries ∧ dirs1[ino].nsubdirs = # subdirs(ino, dirs1)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs1 ∧ files1[ino].nlink = # links(ino, dirs1)) ∧ (ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → valid-ino(dirs1[ino].entries[name], dirs1, files1)) ∧ (ino ∈ files1 ∧ n ∈ files1[ino].content → valid-pagesize(ino, n, files1))))
Proof step 421:
VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m2, md0, # links(m, dirs), content), dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons (of, dirs, files [m, mkfile (m2, md0, # links(m, dirs), content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1))]) ]), of-cons(of, dirs, files0), of-cons(of, dirs, files), m ∈ files, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, fd ∈ of, m ∈ files0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n1) ≤ VFS_PAGE_SIZE, ino0 + min(n0 - ino0, n1) ≤ # buf0, ino0 ≤ n0, n0 ≤ # buf0, ino0 ≤ # buf0 ⊦ min(n0 - ino0, n1) = 0, n0 = 0, ∀ ino, name, n. ROOT_INO ∈ dirs ∧ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files0)) ∧ ( ino ∈ dirs → ¬ ino ∈ files0 ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files0 → ¬ ino ∈ dirs ∧ files0[ino].nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files0)) ∧ (ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) → ROOT_INO ∈ dirs ∧ ( ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty (ino, dirs, files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ])) ∧ ( ino ∈ dirs → ¬ ino ∈ files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ] ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ ( ino ∈ files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ] → ¬ ino ∈ dirs ∧ files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ] [ino ] .nlink = # links(ino, dirs)) ∧ ( ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino (dirs[ino].entries[name], dirs, files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ])) ∧ ( ino ∈ files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ] ∧ n ∈ files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ] [ino ] .content → valid-pagesize (ino, n, files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ])), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: afs-asm name: afs-cons-reduce seq: ⊦ afs-cons(dirs0, files0) → ( afs-cons(dirs1, files1) ↔ (∀ ino, name, n. ROOT_INO ∈ dirs0 ∧ ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → dir-empty(ino, dirs0, files0)) ∧ ( ino ∈ dirs0 → ¬ ino ∈ files0 ∧ dirs0[ino].nlink = # links(ino, dirs0) ∧ dirs0[ino].nlink ≤ 1 ∧ dirs0[ino].size = # dirs0[ino].entries ∧ dirs0[ino].nsubdirs = # subdirs(ino, dirs0)) ∧ ( ino ∈ files0 → ¬ ino ∈ dirs0 ∧ files0[ino].nlink = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ name ∈ dirs0[ino].entries → valid-ino (dirs0[ino].entries[name], dirs0, files0)) ∧ ( ino ∈ files0 ∧ n ∈ files0[ino].content → valid-pagesize(ino, n, files0)) → ROOT_INO ∈ dirs1 ∧ ( ino ∈ dirs1 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs1) = ∅ → dir-empty(ino, dirs1, files1)) ∧ ( ino ∈ dirs1 → ¬ ino ∈ files1 ∧ dirs1[ino].nlink = # links(ino, dirs1) ∧ dirs1[ino].nlink ≤ 1 ∧ dirs1[ino].size = # dirs1[ino].entries ∧ dirs1[ino].nsubdirs = # subdirs(ino, dirs1)) ∧ ( ino ∈ files1 → ¬ ino ∈ dirs1 ∧ files1[ino].nlink = # links(ino, dirs1)) ∧ ( ino ∈ dirs1 ∧ name ∈ dirs1[ino].entries → valid-ino (dirs1[ino].entries[name], dirs1, files1)) ∧ ( ino ∈ files1 ∧ n ∈ files1[ino].content → valid-pagesize(ino, n, files1)))) subst: [dirs0, files0, files1, dirs1] → [dirs, files0, files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy (buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ], dirs] flags: <all paths>

Additional information

Used terms: dirs, files0, files [m, mkfile (m2, md0, # links(m, dirs), content [(m0 + ino0) / VFS_PAGE_SIZE, copy (buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(n0 - ino0, n1)) ]) ], dirs