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Proof step 139 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m2, md0, # links(m, dirs), content), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files1), 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, n3))]) ]), of-cons(of, dirs, files1), of-cons(of, dirs, files), m ∈ files, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n3) ≤ VFS_PAGE_SIZE, ino0 + min(n0 - ino0, n3) ≤ # buf0, ino0 ≤ n0, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino0 ≤ # buf0 ⊦ min(n0 - ino0, n3) = 0, n0 = 0, n2 = 0, ∀ ino, name, n. ROOT_INO ∈ dirs ∧ (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dir-empty(ino, dirs, files1)) ∧ ( ino ∈ dirs → ¬ ino ∈ files1 ∧ dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs)) ∧ (ino ∈ files1 → ¬ ino ∈ dirs ∧ files1[ino].nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → valid-ino(dirs[ino].entries[name], dirs, files1)) ∧ (ino ∈ files1 ∧ n ∈ files1[ino].content → valid-pagesize(ino, n, files1)) → 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, n3)) ]) ])) ∧ ( 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, n3)) ]) ] ∧ 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, n3)) ]) ] → ¬ 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, n3)) ]) ] [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, n3)) ]) ])) ∧ ( 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, n3)) ]) ] ∧ 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, n3)) ]) ] [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, n3)) ]) ])), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 140:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files[m] = mkfile(m2, md0, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files), of-cons(of, dirs, files1), 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, n3))]) ]), ROOT_INO ∈ dirs, m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, m ∈ files, ino0 ≤ # buf0, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, ino0 ≤ n0, ino0 + min(n0 - ino0, n3) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n3) ≤ VFS_PAGE_SIZE, ino ∈ files1 → ¬ ino ∈ dirs ∧ files1[ino].nlink = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files1, ino ∈ files1 ∧ n ∈ files1[ino].content → # files1[ino].content[n] = VFS_PAGE_SIZE ⊦ min(n0 - ino0, n3) = 0, n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, ( ino ∈ files → ¬ ino ∈ dirs ∧ (ino = 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, n3)) ]) ;files[ino] ) .nlink = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files) ∧ ( ino ∈ files ∧ n ∈ (ino = 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, n3)) ]) ;files[ino] ) .content → # (ino = 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, n3)) ]) ;files[ino] ) .content [n ] = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) → ROOT_INO ∈ dirs; (ss)%⊦ valid-pagesize(ino, n, files) ↔ # files[ino].content[n] = VFS_PAGE_SIZE; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)