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Proof step 101 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), buf = buf0, err = ESUCCESS, ino = (ino2 + ino0) % VFS_PAGE_SIZE, ino0 = ino4, ino1 = m0 + n0, ino2 = m0, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), ¬ isdir, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, n = min(ino1 - ino2 + ino0, VFS_PAGE_SIZE - ino), pageno = (ino2 + ino0) / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, VFS_PAGE_SIZE ≥ ino, ino1 ≥ ino2 + ino0 ⊦ [vfs_writepage#(inode, pageno, buf, ino0, ino, n, dirs; err, files, asynced); if err = ESUCCESS then ino0 := ino0 + n] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), VFS_PAGE_SIZE = 0, n = 0, n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 102:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), err = ESUCCESS, m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, min(n0 - ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE) ≠ 0, n0 ≠ 0, n2 ≠ 0, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino0 ≤ n0, ino0 ≤ # buf0 ⊦ [vfs_writepage# (mkinode(m, md, false, # links(m, dirs), 0, m1), (m0 + ino0) / VFS_PAGE_SIZE, buf0, ino0, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE), dirs ; err, files, asynced); if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, VFS_PAGE_SIZE - (m0 + ino0) % VFS_PAGE_SIZE)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n - n + n1 = m - n1; (s)