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Proof step 27 from proof inv-truncate (previous step)

files0[m] = mkfile(m1, md1, # links(m, dirs), content0), content = files0[inode.ino].content, files = files0[ino, files0[ino].content:= (content[pageno, fill(buf-opt.buf, zero, old_ino0, VFS_PAGE_SIZE - old_ino0)] upto old_ino)], ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), new_inode = inode, old_ino = min(n, inode.size), old_ino0 = inode.size % VFS_PAGE_SIZE, old_ino1 = 0, old_ino2 = 0, pageno = m2 / VFS_PAGE_SIZE, buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, inode.size ≤ n, old_ino0 + (VFS_PAGE_SIZE - old_ino0) ≤ # buf-opt.buf, VFS_PAGE_SIZE ≥ old_ino0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, pageno ∈ content ∨ buf-opt.some? ⊦ ⟪afs_inode_sync#(new_inode.size:= n; dirs, files); inode := getinode(inode.ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), VFS_PAGE_SIZE = 0, old_ino0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# buf-opt.buf = VFS_PAGE_SIZE, files0[m] = mkfile(m1, md1, # links(m, dirs), content0), files = files0 [m, mkfile (m1, md1, # links(m, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2) ], inode = mkinode(m, md, false, # links(m, dirs), 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, afs-cons(dirs, files0), m ∈ files0, m2 ≤ n ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, dirs), 0, n); dirs, files); 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, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ mkinode(m, md, boolvar, m0, m1, m2).size:= m6 = mkinode(m, md, boolvar, m0, m1, m6); (s)%min-comm: ⊦ min(n0, n1) = min(n1, n0); from specification min-max% ⊦ n0 ≤ n1 → min(n0, n1) = n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)