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Proof step 2 from proof inv-renam (previous step)

fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log) ⊦ ⟪aubifs_rename#(fi, fo; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar)⟫ ( ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes?)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
old_child_inode.ino = old_dent.ino, fs[ri[dentrykey(old_parent_inode.ino, old_dent.name)]].ino = old_dent.ino, old_parent_inode.nlink = fs[ri[inodekey(old_parent_inode.ino)]].nlink, new_parent_inode.nlink = fs[ri[inodekey(new_parent_inode.ino)]].nlink, old_parent_inode.nsubdirs = fs[ri[inodekey(old_parent_inode.ino)]].nsubdirs, new_parent_inode.nsubdirs = fs[ri[inodekey(new_parent_inode.ino)]].nsubdirs, old_parent_inode.size = fs[ri[inodekey(old_parent_inode.ino)]].size, new_parent_inode.size = fs[ri[inodekey(new_parent_inode.ino)]].size, old_parent_inode.size ≠ 0, old_dent.dentry?, old_parent_inode.directory, new_parent_inode.directory, fs[ri[inodekey(new_parent_inode.ino)]].directory, fs[ri[inodekey(old_parent_inode.ino)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(new_parent_inode.ino) ∈ ri, dentrykey(old_parent_inode.ino, old_dent.name) ∈ ri, inodekey(old_dent.ino) ∈ ri, inodekey(old_parent_inode.ino) ∈ ri, 1 ≤ old_parent_inode.size, ¬ inodekey(old_parent_inode.ino) ∈ ro, old_child_inode.directory → 1 ≤ old_parent_inode.nsubdirs, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, old_parent_inode.nlink ≠ 0 ∨ old_parent_inode.ino = ROOT_INO, new_dent.negdentry? ∧ (new_parent_inode.nlink ≠ 0 ∨ new_parent_inode.ino = ROOT_INO) ∧ ¬ inodekey(new_parent_inode.ino) ∈ ro ∧ ¬ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∨ new_dent.dentry? ∧ (new_parent_inode.nlink ≠ 0 ∨ new_parent_inode.ino = ROOT_INO) ∧ ¬ inodekey(new_parent_inode.ino) ∈ ro ∧ inodekey(new_dent.ino) ∈ ri ∧ dentrykey(new_parent_inode.ino, new_dent.name) ∈ ri ∧ fs[ri[dentrykey(new_parent_inode.ino, new_dent.name)]].ino = new_dent.ino ∧ ( inodekey(new_child_inode.ino) ∈ ri ∧ ¬ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ ¬ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∨ inodekey(new_child_inode.ino) ∈ ri ∧ fs[ri[inodekey(new_child_inode.ino)]].directory ∧ new_child_inode.directory ∧ new_child_inode.nlink = fs[ri[inodekey(new_child_inode.ino)]].nlink ∧ new_child_inode.nsubdirs = fs[ri[inodekey(new_child_inode.ino)]].nsubdirs ∧ new_child_inode.size = fs[ri[inodekey(new_child_inode.ino)]].size) ∧ new_child_inode.ino = new_dent.ino ∧ (¬ fs[ri[inodekey(new_dent.ino)]].directory ↔ ¬ fs[ri[inodekey(old_dent.ino)]].directory) ∧ (fs[ri[inodekey(new_dent.ino)]].directory → new_dent.ino ≠ ROOT_INO ∧ dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_child_inode.ino ≠ ROOT_INO ∧ new_child_inode.nlink ≠ 0 ∧ (new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = ∅ ++ dentrykey(new_parent_inode.ino, new_dent.name)), ¬ fs[ri[inodekey(old_dent.ino)]].directory ∧ ¬ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_dent.ino)]].nsubdirs ∨ fs[ri[inodekey(old_dent.ino)]].directory ∧ old_child_inode.directory ∧ old_child_inode.nlink = fs[ri[inodekey(old_dent.ino)]].nlink ∧ old_child_inode.nsubdirs = fs[ri[inodekey(old_dent.ino)]].nsubdirs ∧ old_child_inode.size = fs[ri[inodekey(old_dent.ino)]].size ⊦ ⟪aubifs_rename#(fi, fo; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar)⟫ (ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro))

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%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-inj(ri); (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ {key} = ∅ ++ key; (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)%⊦ 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-wb-inode(inode, fs, ri) ↔ valid-file-inode(inode, fs, ri) ∨ valid-dir-inode(inode, fs, ri); (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (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-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)%⊦ valid-negdentry(ino, dent, fs, ri, ro) ↔ dent.negdentry? ∧ valid-parent-ino(ino, fs, ri, ro) ∧ ¬ dentrykey(ino, dent.name) ∈ ri; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, fs, ri, ro) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∨ valid-dentry(new_parent_inode.ino, new_dent, fs, ri, ro) ∧ valid-wb-inode(new_child_inode, fs, ri) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, fs, ri) ↔ valid-file-ino(old_dent.ino, fs, ri)) ∧ ( valid-dir-ino(new_dent.ino, fs, ri) → new_dent.ino ≠ ROOT_INO ∧ dentrykeys(inodekey(new_dent.ino), ri) = ∅) ∧ new_child_inode.ino ≠ ROOT_INO ∧ new_child_inode.nlink ≠ 0 ∧ ( new_child_inode.nlink = 1 → links(new_child_inode.ino, fs, ri) = {dentrykey(new_parent_inode.ino, new_dent.name)} )) ∧ valid-dentry(old_parent_inode.ino, old_dent, fs, ri, ro) ∧ valid-dir-inode(new_parent_inode, fs, ri) ∧ valid-dir-inode(old_parent_inode, fs, ri) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, fs, ri) ∧ old_child_inode.ino = old_dent.ino ∧ old_parent_inode.size ≥ 1 ∧ (old_child_inode.directory → old_parent_inode.nsubdirs ≥ 1); (s)