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Proof step 169 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?, n3 < VFS_PAGE_SIZE, dom of < ino3, n1 < VFS_PAGE_SIZE, m0 * VFS_PAGE_SIZE + n3 < 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 ≤ m0 * VFS_PAGE_SIZE + n3 ⊃ zero;(m0 ∈ content0 ⊃ content0[m0];zeropage)[n3]) = (m0 * VFS_PAGE_SIZE < m1 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content0 ⊃ content0[m1, fill(content0[m1], zero, n1, n0)][m0];zeropage)[n3], n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 170:
⊦ n ≠ n0 → content[n0, buf][n] = content[n]
Proof step 171:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), m0 = m1, root.dir?, m0 * VFS_PAGE_SIZE + n3 < n, n1 < VFS_PAGE_SIZE, dom of < ino3, n3 < VFS_PAGE_SIZE, 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 ≤ m0 * VFS_PAGE_SIZE + n3 ⊃ zero;(m0 ∈ content0 ⊃ content0[m0];zeropage)[n3]) = (m0 * VFS_PAGE_SIZE < m1 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content0 ⊃ content0[m1, fill(content0[m1], zero, n1, n0)][m0];zeropage)[n3], n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs
Proof step 174:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, m0 * VFS_PAGE_SIZE + n3 < n, n1 < VFS_PAGE_SIZE, dom of < ino3, n3 < VFS_PAGE_SIZE, 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 ≤ m0 * VFS_PAGE_SIZE + n3 ⊃ zero;(m0 ∈ content0 ⊃ content0[m0];zeropage)[n3]) = (m0 * VFS_PAGE_SIZE < m1 * VFS_PAGE_SIZE + n1 ∧ m0 ∈ content0 ⊃ content0[m0];zeropage)[n3], m0 = m1, n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

Rule argument

spec: store, inst: file-content name: At-other seq: ⊦ n ≠ n0 → content[n0, buf][n] = content[n] subst: [n, buf, n0, content] → [m0, fill(content0[m1], zero, n1, n0), m1, content0] flags: <all paths>

Additional information

Used terms: m0, fill(content0[m1], zero, n1, n0), m1, content0