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Proof step 156 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, dom of < ino3, n1 < VFS_PAGE_SIZE, n2 < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m1 ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m1 * VFS_PAGE_SIZE + n1 ≤ n, psynced0 → asynced0 ⊦ (m1 * VFS_PAGE_SIZE + n1 ≤ n2 ⊃ zero;getbyte(n2, content0)) = getpage(n2 / VFS_PAGE_SIZE, content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))[n2 % VFS_PAGE_SIZE], n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 157:
⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage)
Proof step 158:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, n2 < n, n1 < VFS_PAGE_SIZE, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), afs-cons(dirs, files1), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), of-cons(of, dirs, files1), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), ROOT_INO ∈ dirs, ino2 ∈ files1, m1 ∈ content0, m1 * VFS_PAGE_SIZE + n1 ≤ n, psynced0 → asynced0 ⊦ (m1 * VFS_PAGE_SIZE + n1 ≤ n2 ⊃ zero;getbyte(n2, content0)) = (n2 / VFS_PAGE_SIZE ∈ content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1) ⊃ (content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))[n2 / VFS_PAGE_SIZE] ;zeropage ) [n2 % VFS_PAGE_SIZE ], n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

Rule argument

spec: afs-stream name: getpage seq: ⊦ getpage(n, content) = (n ∈ content ⊃ content[n];zeropage) subst: [content, n] → [ content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1), n2 / VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used terms: content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1), n2 / VFS_PAGE_SIZE