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Proof step 6 from proof refine-lookup (previous step)

boolvar0 ↔ boolvar1, dent = old_dent, err = err0, ro = orphans(fs, ri), fs[ri[inodekey(p_ino)]].directory, orphans(fs, ri).inodes?, fo.inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), pre-lookup(p_ino, dent, fs, ri, ro), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_ino) ∈ ri, asynced → boolvar1, links(p_ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪err := ESUCCESS; key := dentrykey(p_ino, dent.name); aubifs_core_index_lookup#(key, ri, fi, ro, fo, fs, log, boolvar0; boolvar, nd; err); if err = ESUCCESS then if boolvar then dent := mkdentry(dent.name, nd.ino), err := ESUCCESS else dent := negdentry(dent.name), err := ENOENT⟫ ⟨afs_lookup#(p_ino, abs-dirs(fs, ri), abs-files(fs, ri), asynced; old_dent, err0)⟩ ((asynced → boolvar1) ∧ dent = old_dent ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
fs[ri[inodekey(p_ino)]].directory, fo.inodes?, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, orphans(fs, ri)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(p_ino) ∈ ri, asynced → boolvar1, links(p_ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_ino = ROOT_INO, fs[ri[inodekey(p_ino)]].nlink ≠ 0 ∨ p_ino = ROOT_INO ⊦ ⟪err := ESUCCESS; key := dentrykey(p_ino, old_dent.name); aubifs_core_index_lookup#(key, ri, fi, orphans(fs, ri), fo, fs, log, boolvar1; boolvar, nd; err); dent := old_dent; if err = ESUCCESS then if boolvar then dent := mkdentry(dent.name, nd.ino), err := ESUCCESS else dent := negdentry(dent.name), err := ENOENT⟫ ⟨afs_lookup#(p_ino, abs-dirs(fs, ri), abs-files(fs, ri), asynced; old_dent, err0)⟩ ((asynced → boolvar1) ∧ dent = old_dent ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)%⊦ valid-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, fs, ri, ro) ↔ ( valid-dir-ino(ino, fs, ri) ∧ (fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO)) ∧ ¬ inodekey(ino) ∈ ro; (s)%⊦ pre-lookup(p_ino, dent, fs, ri, ro) ↔ valid-parent-ino(p_ino, fs, ri, ro); (s)