[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 81 from proof truncate-inv (previous step)

files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), content[pageno, fill(files2[ino4].content[pageno], zero, n0, VFS_PAGE_SIZE - n0)] = content2, buf-opt = none, content = content0, fill(files2[ino4].content[pageno], zero, n0, VFS_PAGE_SIZE - n0) = buf0, pageno = m2, pageno = pageno1, some(fill(files2[ino4].content[pageno], zero, n0, VFS_PAGE_SIZE - n0)) = buf-opt0, n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons(dirs0, files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content2 upto (m2 * VFS_PAGE_SIZE + n0))]), files2 ~ files2[ino4, mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content2 upto (m2 * VFS_PAGE_SIZE + n0))], ino4 ∈ files2, m2 ∈ content0, pageno ∈ files2[ino4].content, n0 + (VFS_PAGE_SIZE - n0) ≤ # files2[ino4].content[pageno], VFS_PAGE_SIZE ≥ n0 ⊦ (content2.stream to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 82:
files2[ino4] = mkfile(m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0), n0 < VFS_PAGE_SIZE, afs-cons(dirs0, files2), afs-cons (dirs0, files2 [ino4, mkfile (m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)] upto (m2 * VFS_PAGE_SIZE + n0)) ]), files2 ~ files2 [ino4, mkfile (m2 * VFS_PAGE_SIZE + n0, md, # links(ino4, dirs0), content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)] upto (m2 * VFS_PAGE_SIZE + n0)) ], ino4 ∈ files2, m2 ∈ content0 ⊦ (content0[m2, fill(content0[m2], zero, n0, VFS_PAGE_SIZE - n0)].stream to VFS_PAGE_SIZE * m2 + VFS_PAGE_SIZE) + σ⊥ from m2 * VFS_PAGE_SIZE + n0 = σ⊥, n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n < m → (m - n) + n = m; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)