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Proof step 242 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root.dir?, n0 < n, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), 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, m0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, psynced0 → asynced0 ⊦ (m0 ≤ n0 ⊃ zero;getpage(n0 / VFS_PAGE_SIZE, content0)[n0 % VFS_PAGE_SIZE]) = getpage(n0 / VFS_PAGE_SIZE, content0 upto min(n, m0))[n0 % VFS_PAGE_SIZE], root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 243:
⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage)
Proof step 244:
files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root.dir?, dom of < ino3, n0 < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), 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, m0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, psynced0 → asynced0 ⊦ (m0 ≤ n0 ⊃ zero;(n0 / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]) = getpage(n0 / VFS_PAGE_SIZE, content0 upto min(n, m0))[n0 % VFS_PAGE_SIZE], root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Rule argument

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

Additional information

Used terms: content0, n0 / VFS_PAGE_SIZE