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Proof step 28 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0 [m, mkfile (m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, m2 ≤ n ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0[m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, m2 ≤ n, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), m2 % VFS_PAGE_SIZE = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n0]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n0