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Proof step 58 from proof refine-writemeta (previous step)

dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), fs = abs-files(files), root.dir?, root[path].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced → asynced0 ⊦ pw(user, path, root, fs) ∧ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then if root[path].dir? then root[path].meta := md else let fid = root[path].fid in fs[fid] := mkfile(md, fs[fid].content); psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 59:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)))
Proof step 60:
dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), fs = abs-files(files), root[path].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced → asynced0 ⊦ ⟨err0 := ESUCCESS; if err0 = ESUCCESS then if root[path].dir? then root[path].meta := md else let fid = root[path].fid in fs[fid] := mkfile(md, fs[fid].content); psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: pw: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( pw(user, p, tree, abs-files(files)) ↔ pw(user, meta(ε, m, dirs, files)));% ⊦ ino ∈ dirs → meta(ε, ino, dirs, files) = dirs[ino].meta; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)