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Proof step 135 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files1[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), files[m] = mkfile(m2, md0, m3, content), buf = copy(buf0, ino0, content[(m0 + ino0) / VFS_PAGE_SIZE], (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, n3)), err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, pageno = (m0 + ino0) / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files1), afs-cons(dirs, files), of-cons(of, dirs, files1), of-cons(of, dirs, files), pre-writepage(inode, pageno, buf, dirs, files), (m0 + ino0) / VFS_PAGE_SIZE ∈ content, fd ∈ of, m1 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, ino0 ≤ n0, n2 + n1 ≤ VFS_PAGE_SIZE, n0 ≤ # buf0, ino0 ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n3) ≤ # content[(m0 + ino0) / VFS_PAGE_SIZE], ino0 + min(n0 - ino0, n3) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(m0 + n0 - m0 + ino0, n3) ≤ # content[(m0 + ino0) / VFS_PAGE_SIZE], ino0 + min(m0 + n0 - m0 + ino0, n3) ≤ # buf0, m0 + n0 ≥ m0 + ino0 ⊦ VFS_PAGE_SIZE = 0, min(n0 - ino0, n3) = 0, n0 = 0, n2 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, of-cons(of, dirs, files[inode.ino, files[inode.ino].content:= files[inode.ino].content[pageno, buf]]) ∧ afs-cons(dirs, files[inode.ino, files[inode.ino].content:= files[inode.ino].content[pageno, buf]])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 137:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, VFS_PAGE_SIZE = n3 + (m0 + ino0) % VFS_PAGE_SIZE, files[m] = mkfile(m2, md0, # links(m, dirs), content), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md, # links(m, dirs), content0), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), 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, n3))]) ]), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, (m0 + ino0) / VFS_PAGE_SIZE ∈ content, m ∈ files, ino0 ≤ # buf0, n0 ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE, ino0 ≤ n0, ino0 + min(n0 - ino0, n3) ≤ # buf0, (m0 + ino0) % VFS_PAGE_SIZE + min(n0 - ino0, n3) ≤ VFS_PAGE_SIZE ⊦ min(n0 - ino0, n3) = 0, n0 = 0, n2 = 0, afs-cons (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, n3))]) ]), mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (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%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-writepage(inode, n, buf, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ # buf = VFS_PAGE_SIZE; (s)% ⊦ m + n - n + n1 = m - n1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)