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Proof step 78 from proof inv-truncate (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m1, md1, # links(m, dirs), content0), files0 = files [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, afs-cons (dirs, files [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files), m ∈ files, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ n, ¬ buf-opt.some? ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files0)] ( afs-cons(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 := ?⟫ true)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 79:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0, files0 = files1 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, n), inode0 = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files1), afs-cons (dirs, files1 [m, mkfile(m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files1, m2 ≤ n ⊦ [let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta] ( afs-cons(dirs, files) → ⟪inode0 := (inode0.ino ∈ dirs ⊃ mkinode(inode0.ino, dirs[inode0.ino].meta, true, dirs[inode0.ino].nlink, dirs[inode0.ino].nsubdirs, dirs[inode0.ino].size) ;mkinode(inode0.ino, files[inode0.ino].meta, false, files[inode0.ino].nlink, 0, files[inode0.ino].size) ); err := ESUCCESS; asynced := ?⟫ true), m2 % VFS_PAGE_SIZE = 0, buf-opt.some?

Rule argument

pos: right 1

Additional information

Used simplifier rules: internal-inode-sync: ⊦ ;