[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 248 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, n0 < VFS_PAGE_SIZE, m1 * VFS_PAGE_SIZE + n1 < n, dom of < ino3, n1 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, psynced0 → asynced0 ⊦ (m2 * VFS_PAGE_SIZE + n0 ≤ m1 * VFS_PAGE_SIZE + n1 ⊃ zero;(m1 ∈ content0 ⊃ content0[m1];zeropage)[n1]) = getpage(m1, content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))[n1], root[path].dir?, ino2 ∈ dirs, m2 * VFS_PAGE_SIZE + n0 ≤ n ∧ n0 ≠ 0 ∧ m2 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 249:
⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage)
Proof step 250:
files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, n1 < VFS_PAGE_SIZE, dom of < ino3, m1 * VFS_PAGE_SIZE + n1 < n, n0 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))]), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, psynced0 → asynced0 ⊦ (m2 * VFS_PAGE_SIZE + n0 ≤ m1 * VFS_PAGE_SIZE + n1 ⊃ zero;(m1 ∈ content0 ⊃ content0[m1];zeropage)[n1]) = (m1 ∈ content0 upto min(n, m2 * VFS_PAGE_SIZE + n0) ⊃ (content0 upto min(n, m2 * VFS_PAGE_SIZE + n0))[m1];zeropage)[n1], root[path].dir?, ino2 ∈ dirs, m2 * VFS_PAGE_SIZE + n0 ≤ n ∧ n0 ≠ 0 ∧ m2 ∈ content0

Rule argument

spec: afs-stream name: getpage seq: ⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage) subst: [content, n] → [content0 upto min(n, m2 * VFS_PAGE_SIZE + n0), m1] flags: <all paths>

Additional information

Used terms: content0 upto min(n, m2 * VFS_PAGE_SIZE + n0), m1