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

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, # links(m, dirs), content0), files1 = files [m, mkfile(m0, md0, # 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), afs-cons(dirs, files), m2 / VFS_PAGE_SIZE ∈ content0, m ∈ files, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, m2); dirs, files1); 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, files1[inode.ino].meta, false, files1[inode.ino].nlink, 0, files1[inode.ino].size) ); err := ESUCCESS; asynced := ?] (err = ESUCCESS ⊃ files1[inode.ino].content.stream to files1[inode.ino].size = files[inode.ino].content.stream to files1[inode.ino].size ∧ inode.ino ∈ files1 ∧ m2 = files1[inode.ino].size ∧ files[inode.ino].nlink = files1[inode.ino].nlink ∧ files -- inode.ino = files1 -- inode.ino ;⌊err⌋ ∧ files = files1 ), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, # links(m, dirs), content0), files1 = files [m, mkfile(m0, md0, # 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 ∈ files, m2 / VFS_PAGE_SIZE ∈ content0 ⊦ [afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, m2); dirs, files1); 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, files1[inode.ino].meta, false, files1[inode.ino].nlink, 0, files1[inode.ino].size) ); err := ESUCCESS; asynced := ?] (err = ESUCCESS ⊃ files1[inode.ino].content.stream to files1[inode.ino].size = files[inode.ino].content.stream to files1[inode.ino].size ∧ inode.ino ∈ files1 ∧ m2 = files1[inode.ino].size ∧ files[inode.ino].nlink = files1[inode.ino].nlink ∧ files -- inode.ino = files1 -- inode.ino ;⌊err⌋ ∧ files = files1 )

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)