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

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Proof step 422 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, files0), afs-cons(dirs, files), 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))]) ]), ROOT_INO ∈ dirs, 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, ino ∈ files0 → ¬ ino ∈ dirs ∧ files0[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] ∈ files0, ino ∈ files0 ∧ n ∈ files0[ino].content → # files0[ino].content[n] = VFS_PAGE_SIZE ⊦ min(n0 - ino0, n1) = 0, n0 = 0, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, 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, n1)) ]) ;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, n1)) ]) ;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, n1)) ]) ;files[ino] ) .content [n ] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 423:
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), files0[ino] = mkfile(m3, md1, m4, content1), 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, ROOT_INO ∈ dirs, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n1) ≤ VFS_PAGE_SIZE, ino0 + min(n0 - ino0, n1) ≤ # buf0, ino0 ≤ n0, n0 ≤ # buf0, ino0 ≤ # buf0, ino ∈ files0 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files0, 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 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs) ⊦ min(n0 - ino0, n1) = 0, n0 = 0, ( 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, n1)) ]) ;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, n1)) ]) ;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, n1)) ]) ;files[ino] ) .content [n ] = VFS_PAGE_SIZE), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files0[ino], m3, md1, m4, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files0[ino], m3, md1, m4, content1