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Proof step 38 from proof refine-link (previous step)

fs[ri[dentrykey(ino1, str)]].ino = p_inode1.ino, p_inode1.ino = fs[ri[dentrykey(ino0, str)]].ino, p_inode0.nlink = fs[ri[inodekey(p_inode0.ino)]].nlink, p_inode1.nlink = fs[ri[inodekey(p_inode1.ino)]].nlink, p_inode0.nsubdirs = fs[ri[inodekey(p_inode0.ino)]].nsubdirs, p_inode1.nsubdirs = 0, p_inode0.size = fs[ri[inodekey(p_inode0.ino)]].size, 0 = fs[ri[inodekey(p_inode1.ino)]].nsubdirs, c_inode = p_inode1, dirs = abs-dirs(fs, ri), err = err0, files = abs-files(fs, ri), ino = c_inode.ino, new_dent = negdentry(str0), old_dent = mkdentry(str, p_inode1.ino), p_inode = p_inode0, ro = orphans(fs, ri), ro0 = orphans(fs, ri), fs[ri[inodekey(ino1)]].directory, fs[ri[inodekey(p_inode0.ino)]].directory, p_inode0.directory, fs[ri[inodekey(ino0)]].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)), pre-link(p_inode, c_inode, old_dent, new_dent, fs, ri, ro), 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(ino1) ∈ ri, inodekey(p_inode1.ino) ∈ ri, dentrykey(ino1, str) ∈ ri, inodekey(p_inode0.ino) ∈ ri, inodekey(ino0) ∈ ri, dentrykey(ino0, str) ∈ ri, asynced → boolvar, fs[ri[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, p_inode0.nlink ≠ 0 ∨ p_inode0.ino = ROOT_INO, links(ino0, abs-dirs(fs, ri)) ≠ ∅ ∨ ino0 = ROOT_INO, links(p_inode0.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode0.ino = ROOT_INO, links(p_inode1.ino, abs-dirs(fs, ri)) ≠ ∅ ∨ p_inode1.ino = ROOT_INO ⊦ [key0 := dentrykey(p_inode.ino, new_dent.name); key := inodekey(ino); nd1 := inodenode(inodekey(p_inode.ino), p_inode.meta, p_inode.directory, p_inode.nlink, p_inode.nsubdirs, p_inode.size + 1); nd0 := dentrynode(key0, ino); nd := inodenode(key, c_inode.meta, c_inode.directory, c_inode.nlink + 1, c_inode.nsubdirs, c_inode.size); aubifs_core_journal_add3#(nd1, nd0, nd, ri, fi, ro, fo; adr1, adr0, adr, fs, log; boolvar, err); if err = ESUCCESS then {aubifs_core_index_store#(inodekey(p_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key0, adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); new_dent := mkdentry(new_dent.name, ino); p_inode := mkinode(p_inode.ino, nd1.meta, nd1.directory, nd1.nlink, nd1.nsubdirs, nd1.size); c_inode := mkinode(ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}] ( ubifs-cons(fs, ri, ro0, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro0, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro0) ∧ ri-inj(ri) ∧ log-cons(log, fs) → ⟨old_dent0 := negdentry(str0); afs_link#(mkdentry(str, p_inode1.ino); p_inode0, p_inode1, old_dent0, err0, dirs, files; asynced)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro0) ∧ (asynced → boolvar) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0)), fs[ri[inodekey(p_inode1.ino)]].directory, p_inode1.directory, dentrykey(p_inode0.ino, str0) ∈ ri, p_inode1.nlink = 0 ∧ p_inode1.ino ≠ ROOT_INO, p_inode0.nlink = 0 ∧ p_inode0.ino ≠ ROOT_INO, fs[ri[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ubifs-parent-in: ⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%⊦ valid-file-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-file-inode(inode, fs, ri) ↔ valid-file-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs; (s)%⊦ valid-dir-inode(inode, fs, ri) ↔ valid-dir-ino(inode.ino, fs, ri) ∧ (inode.directory ↔ fs[ri[inodekey(inode.ino)]].directory) ∧ inode.nlink = fs[ri[inodekey(inode.ino)]].nlink ∧ inode.nsubdirs = fs[ri[inodekey(inode.ino)]].nsubdirs ∧ inode.size = fs[ri[inodekey(inode.ino)]].size; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (s)%⊦ valid-negdentry(ino, dent, fs, ri, ro) ↔ dent.negdentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ ¬ dentrykey(ino, dent.name) ∈ ri; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ 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)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ valid-dentry(ino, dent, fs, ri, ro) ↔ dent.dentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ valid-ino(dent.ino, fs, ri) ∧ dentrykey(ino, dent.name) ∈ ri ∧ fs[ri[dentrykey(ino, dent.name)]].ino = dent.ino; (s)%⊦ valid-dentry(dent, fs, ri, ro) ↔ (∃ ino. valid-dentry(ino, dent, fs, ri, ro)); (s)%⊦ pre-link(p_inode, c_inode, old_dent, new_dent, fs, ri, ro) ↔ ( valid-dentry(old_dent, fs, ri, ro) ∧ valid-negdentry(p_inode.ino, new_dent, fs, ri, ro) ∧ ¬ inodekey(old_dent.ino) ∈ ro) ∧ valid-dir-inode(p_inode, fs, ri) ∧ valid-file-inode(c_inode, fs, ri) ∧ c_inode.ino = old_dent.ino; (s)