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Proof step 429 from proof inv-write (previous step)

(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] ) = mkfile(m5, md2, m6, content2), VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, dirs[ino] = mkdir(m7, md3, m8, m9, entries), 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 → m4 = # links(ino, dirs) ⊦ min(n0 - ino0, n1) = 0, n0 = 0, ino ∈ dirs, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, (ino ∈ files → m6 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 430:
(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] ) = mkfile(m5, md2, m6, content2), VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files0[ino] = mkfile(m3, md1, m4, content1), files[m] = mkfile(m2, md0, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), dirs[ino] = mkdir(m7, md3, m8, m9, entries), ino = m, 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 → m4 = # links(ino, dirs) ⊦ min(n0 - ino0, n1) = 0, n0 = 0, ino ∈ dirs, (ino ∈ files → m6 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (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 Used formulas: ino = m