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Proof step 29 from proof truncate-empty (previous step)

files[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), files0 = files [ino0, mkfile (m, md0, # links(ino0, dirs), content0[n / VFS_PAGE_SIZE, fill(content0[n / VFS_PAGE_SIZE], zero, n % VFS_PAGE_SIZE, VFS_PAGE_SIZE - n % VFS_PAGE_SIZE)] upto n) ], inode = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), n % VFS_PAGE_SIZE ≠ 0, afs-cons(dirs, files), ino0 ∈ files, n / VFS_PAGE_SIZE ∈ content0 ⊦ [afs_inode_sync#(mkinode(ino0, md1, false, # links(ino0, 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 := ?] (err = ESUCCESS → files0[ino0].content.stream from n = σ⊥)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
VFS_PAGE_SIZE = n0 + n % VFS_PAGE_SIZE, files[ino0] = mkfile(m, md0, # links(ino0, dirs), content0), files0 = files [ino0, mkfile(m, md0, # links(ino0, dirs), content0[n / VFS_PAGE_SIZE, fill(content0[n / VFS_PAGE_SIZE], zero, n % VFS_PAGE_SIZE, n0)] upto n) ], inode = mkinode(ino0, md1, false, # links(ino0, dirs), 0, n), afs-cons(dirs, files), n / VFS_PAGE_SIZE ∈ content0, ino0 ∈ files, n % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(ino0, md1, false, # links(ino0, 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 := ?] (err = ESUCCESS → files0[ino0].content.stream from n = σ⊥), n % VFS_PAGE_SIZE = 0

Rule argument

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