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Proof step 86 from proof inv-truncate (previous step)

files[ino2] = mkfile(m, md, # links(ino2, dirs), content0), files0 = files [ino2, mkfile (m, md, # links(ino2, dirs), content0[m / VFS_PAGE_SIZE, fill(content0[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m % VFS_PAGE_SIZE)] upto m) ], inode = mkinode(ino2, md, false, # links(ino2, dirs), 0, m), m % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files), ispath(p, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md), px-parent(user, p, ROOT_INO, dirs, files), ino2 ∈ files, m / VFS_PAGE_SIZE ∈ content0, m ≤ n, ¬ ino2 ∈ dirs ⊦ [afs_inode_sync#(mkinode(ino2, md, false, # links(ino2, dirs), 0, n); dirs, files0); 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, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files0) → of-cons(of, dirs, files0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 87:
VFS_PAGE_SIZE = n0 + m % VFS_PAGE_SIZE, files[ino2] = mkfile(m, md, # links(ino2, dirs), content0), files0 = files [ino2, mkfile(m, md, # links(ino2, dirs), content0[m / VFS_PAGE_SIZE, fill(content0[m / VFS_PAGE_SIZE], zero, m % VFS_PAGE_SIZE, n0)] upto m) ], inode = mkinode(ino2, md, false, # links(ino2, dirs), 0, m), afs-cons(dirs, files), ispath(p, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md), px-parent(user, p, ROOT_INO, dirs, files), m / VFS_PAGE_SIZE ∈ content0, ino2 ∈ files, m ≤ n, m % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(ino2, md, false, # links(ino2, dirs), 0, n); dirs, files0); 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, files0[inode.ino].meta, false, files0[inode.ino].nlink, 0, files0[inode.ino].size) ); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files0) → of-cons(of, dirs, files0)), m % VFS_PAGE_SIZE = 0, ino2 ∈ dirs

Rule argument

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