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Proof step 248 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md0, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), dirs1 = dirs, err = err0, err0 = ESUCCESS, inode = mkinode(m, md0, false, # links(m, dirs), 0, m0 + ino4), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), pre-write-inode(inode, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE ⊦ ino4 = 0, n = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err1 = ESUCCESS ∧ ¬ isdir, of-cons (of[fd, of[fd].pos:= (m0 + ino4)], dirs, files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ]) ∧ dom of[fd, of[fd].pos:= (m0 + ino4)] < ino3 ∧ afs-cons (dirs, files[inode.ino, files[inode.ino].meta:= inode.meta] [inode.ino, files[inode.ino, files[inode.ino].meta:= inode.meta][inode.ino].size:= inode.size ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 249:
# links(m, dirs) = files[m].nlink, m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md0, files[m].nlink, content0), of[fd] = mkfile(m, mode, m0), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m1 < m0 + ino4, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), m ∈ files, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE ⊦ ino4 = 0, n = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, err1 = ESUCCESS ∧ ¬ isdir, of-cons(of[fd, mkfile(m, mode, m0 + ino4)], dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)]) ∧ afs-cons(dirs, files[m, (files[m].meta:= md0).size:= (m0 + ino4)])

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, mode, m0).pos:= m2 = mkfile(m, mode, m2); (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ fd ∈ of → dom of ++ fd = dom of; (s)% ⊦ dom of[fd, file] = dom of ++ fd; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)