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Proof step 30 from proof truncate-greater (previous step)

VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files[m0] = mkfile(m, md0, # links(m0, dirs), content0), files1 = files [m0, mkfile(m, md0, # links(m0, dirs), content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3) ], inode = mkinode(m0, md, false, # links(m0, dirs), 0, m3), m3 < n, afs-cons(dirs, files), m3 / VFS_PAGE_SIZE ∈ content0, m0 ∈ files, m3 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_inode_sync#(mkinode(m0, md, false, # links(m0, dirs), 0, n); 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 m3) + (σ⊥ to (files1[inode.ino].size - m3)) ∧ inode.ino ∈ files1 ∧ n = files1[inode.ino].size ∧ files[inode.ino].nlink = files1[inode.ino].nlink ∧ files -- inode.ino = files1 -- inode.ino ;⌊err⌋ ∧ files = files1 ), m3 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, files[m0] = mkfile(m, md0, # links(m0, dirs), content0), files1 = files [m0, mkfile(m, md0, # links(m0, dirs), content0[m3 / VFS_PAGE_SIZE, fill(content0[m3 / VFS_PAGE_SIZE], zero, m3 % VFS_PAGE_SIZE, n0)] upto m3) ], inode = mkinode(m0, md, false, # links(m0, dirs), 0, m3), m3 % VFS_PAGE_SIZE ≠ 0, m3 < n, afs-cons(dirs, files), m0 ∈ files, m3 / VFS_PAGE_SIZE ∈ content0 ⊦ [afs_inode_sync#(mkinode(m0, md, false, # links(m0, dirs), 0, n); 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 m3) + (σ⊥ to (files1[inode.ino].size - m3)) ∧ inode.ino ∈ files1 ∧ n = 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)