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Proof step 74 from proof write-loop-term (previous step)

(ino = m ⊃ mkfile (m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ;mkfile(m0, md1, m3, content0) ) = mkfile(m4, md2, m5, content1), VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, dirs[ino] = mkdir(m6, md3, m7, m8, entries), files0[ino] = mkfile(m0, md1, m3, content0), files0[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, files = files0 [m, mkfile (m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, min(n5, n7) ≠ 0, afs-cons(dirs, files0), ROOT_INO ∈ dirs, (n0 + n6) / VFS_PAGE_SIZE ∈ content, m ∈ files0, n6 ≤ # buf1, n5 + n6 ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n6 + min(n5, n7) ≤ # buf1, min(n5, n7) ≤ n5, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0, ino ∈ dirs → m7 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs), ∀ n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced. n2 - n3 + n4 < n5 → files[m] = mkfile(m1, md0, # links(m, dirs), content) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n3, inode, buf, n2, dirs; n4, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink) ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink), (ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files0 ∧ n2 ∈ content1 → # content1[n2] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 75:
(ino = m ⊃ mkfile (m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ;mkfile(m0, md1, m3, content0) ) = mkfile(m4, md2, m5, content1), VFS_PAGE_SIZE = n7 + (n0 + n6) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md0, # links(m, dirs), content), files0[ino] = mkfile(m0, md1, m3, content0), dirs[ino] = mkdir(m6, md3, m7, m8, entries), err = ESUCCESS, files = files0 [m, mkfile (m1, md0, # links(m, dirs), content[(n0 + n6) / VFS_PAGE_SIZE, copy(buf1, n6, content[(n0 + n6) / VFS_PAGE_SIZE], (n0 + n6) % VFS_PAGE_SIZE, min(n5, n7))]) ], ino = m, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), ¬ isdir, n = n6 + min(n5, n7), n1 = n5 + n0 + n6, afs-cons(dirs, files0), m ∈ files0, (n0 + n6) / VFS_PAGE_SIZE ∈ content, ROOT_INO ∈ dirs, min(n5, n7) ≤ n5, n6 + min(n5, n7) ≤ # buf1, (n0 + n6) % VFS_PAGE_SIZE + min(n5, n7) ≤ VFS_PAGE_SIZE, n5 + n6 ≤ # buf1, n6 ≤ # buf1, ino ∈ dirs → m7 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m6 = # entries ∧ m8 = # subdirs(ino, dirs), ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files0, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs ∧ m3 = # links(ino, dirs), ∀ n2, n3, n4, files, m, m1, md0, dirs, content, inode, md, m2, isdir, buf, err, asynced. n2 - n3 + n4 < n5 → files[m] = mkfile(m1, md0, # links(m, dirs), content) ∧ inode = mkinode(m, md, false, # links(m, dirs), 0, m2) ∧ ¬ isdir ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ n4 ≤ # buf ∧ n3 + n4 ≤ n2 ∧ n2 ≤ # buf + n3 → ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n3, inode, buf, n2, dirs; n4, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink) ⊦ ⟪while err = ESUCCESS ∧ ¬ isdir do vfs_write_block#(n0, inode, buf1, n1, dirs; n, isdir, err, files, asynced)⟫ (m ∈ files ∧ # links(m, dirs) = files[m].nlink), min(n5, n7) = 0, (ino ∈ files0 → ¬ ino ∈ dirs ∧ m5 = # links(ino, dirs)) ∧ (ino ∈ files0 ∧ n2 ∈ content1 → # content1[n2] = VFS_PAGE_SIZE)

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s) Used formulas: ino = m