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Proof step 473 from proof inv-write (previous step)

(ino = m ⊃ mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n2, n1))]) ;files[ino] ) = mkfile(m6, md2, m7, content2), VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, dirs[ino] = mkdir(m8, md3, m9, m10, entries), files[m] = mkfile(m2, md0, m3, content), files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files0[ino] = mkfile(m4, md1, m5, content1), dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons (of, dirs, files[m, mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n2, n1))])]), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, ROOT_INO ∈ dirs, ino0 + min(n2, n1) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n2, n1) ≤ VFS_PAGE_SIZE, n2 + ino0 ≤ # buf0, ino0 ≤ # buf0, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs), ino ∈ dirs → m9 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs) ⊦ n2 + ino0 = 0, min(n2, n1) = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, (ino ∈ files → ¬ ino ∈ dirs ∧ m7 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE), mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 474:
(ino = m ⊃ mkfile(m2, md0, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n2, n1))]) ;files[ino] ) = mkfile(m6, md2, m7, content2), VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files0[ino] = mkfile(m4, md1, m5, content1), of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), files[m] = mkfile(m2, md0, m3, content), dirs[ino] = mkdir(m8, md3, m9, m10, entries), 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, m3, content[(m0 + ino0) / VFS_PAGE_SIZE, copy(buf0, ino0, zeropage, (m0 + ino0) % VFS_PAGE_SIZE, min(n2, n1))])]), ROOT_INO ∈ dirs, m ∈ files0, fd ∈ of, ino0 ≤ # buf0, n2 + ino0 ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n2, n1) ≤ VFS_PAGE_SIZE, ino0 + min(n2, n1) ≤ # buf0, ino ∈ dirs → m9 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs), ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0 ⊦ n2 + ino0 = 0, min(n2, n1) = 0, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, ino ∈ dirs, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, (ino ∈ files → ¬ ino ∈ dirs ∧ m7 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content2 → # content2[n] = VFS_PAGE_SIZE)

Rule argument

fma: ino ∈ dirs

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used formulas: ino ∈ dirs