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Proof step 134 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), fs = abs-files(files1), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons (dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), afs-cons(dirs, files1), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons (of, dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), of-cons(of, dirs, files1), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), ROOT_INO ∈ dirs, ino2 ∈ files1, m0 / VFS_PAGE_SIZE ∈ content0, m0 ≤ n, psynced → asynced0 ⊦ pre-truncate(path, n, ESUCCESS, user, root, fs, abs-of(of)) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fid = root[path].fid in let buf = fs[fid].content in fs[fid] := mkfile(fs[fid].meta, resize(buf, n)); psynced := ?⟩ ( fs = abs-files (files1 [ino2, mkfile (n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]) ∧ (psynced → asynced) ∧ ESUCCESS = err0), m0 % VFS_PAGE_SIZE = 0, root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 135:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 136:
VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), fs = abs-files(files1), m0 % VFS_PAGE_SIZE ≠ 0, root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons (dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m0 / VFS_PAGE_SIZE ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m0 ≤ n, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ pw(user, path, root, fs) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then let fid = root[path].fid in let buf = fs[fid].content in fs[fid] := mkfile(fs[fid].meta, resize(buf, n)); psynced := ?⟩ ( fs = abs-files (files1 [ino2, mkfile (n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%⊦ pre-truncate(p, n, ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ ¬ root[p].dir? ∧ pw(user, p, root, fs); (s)