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Proof step 109 from proof refine-create (previous step)

entries[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), fs = abs-files(files), path = q + str ', root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ pre-create(path, md, EEXISTS, user, root, fs, abs-of(of)) ∧ ⟨err0 := EEXISTS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 110:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 111:
entries[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), fs = abs-files(files), path = q + str ', root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ispath(path, ROOT_INO, dirs, files) ∧ ⟨err0 := EEXISTS; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EEXISTS = 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));% ⊦ pre-create(p, md, EEXISTS, user, root, fs, ofh) ↔ p ∈ root; (s)