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Proof step 39 from proof inv-renam (previous step)

¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, new_child_inode = mkinode(fs[ri[dentrykey(m4, str0)]].ino, md0, boolvar4, m1, m2, m3), new_dent = mkdentry(str0, fs[ri[dentrykey(m4, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(m4, str)]].ino), old_parent_inode = mkinode(m4, md, true, fs[ri[inodekey(m4)]].nlink, fs[ri[inodekey(m4)]].nsubdirs, fs[ri[inodekey(m4)]].size), fs[ri[dentrykey(m4, str0)]].ino ≠ ROOT_INO, fs[ri[inodekey(m4)]].size ≠ 0, m1 ≠ 0, fs[ri[inodekey(m4)]].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), dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, inodekey(m4) ∈ ri, inodekey(fs[ri[dentrykey(m4, str0)]].ino) ∈ ri, dentrykey(m4, str0) ∈ ri, 1 ≤ fs[ri[inodekey(m4)]].size, ¬ inodekey(m4) ∈ ro, boolvar → 1 ≤ fs[ri[inodekey(m4)]].nsubdirs, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m4, str0)]].ino), ri) = ∅, m1 = 1 → links(fs[ri[dentrykey(m4, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m4, str0), fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nlink ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nlink ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ m9 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ ¬ boolvar4 ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory ∧ boolvar4 ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].size ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar, mkinode(fs[ri[dentrykey(m4, str)]].ino, md2, boolvar, m0, m8, m9), fi, fo ; old_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar2); new_parent_inode := old_parent_inode⟫ (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))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: inv-rename-overwrite-keep-parent seq: 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), ri-inj(fi), log-cons(log, fs), ro.inodes?, fo.inodes?, pre-rename-overwrite-keep-parent (parent_inode, old_dent, old_child_inode, new_dent, new_child_inode, fs, ri, ro), boolvar ↔ old_child_inode.directory ⊦ ⟪aubifs_rename_overwrite_keep_parent# (boolvar, old_child_inode, fi, fo ; parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)⟫ ( 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?) subst: [fo, fi, old_child_inode, boolvar, boolvar0, log, fs, ro, ri, err, new_dent, old_dent, new_child_inode, parent_inode] → [fo, fi, mkinode (fs[ri[dentrykey(m4, str)]].ino, md2, boolvar, m0, m8, m9), boolvar, boolvar2, log, fs, ro, ri, err, new_dent, old_dent, new_child_inode, old_parent_inode] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ri-inj(ri); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → log-cons(log, fs); (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ro.inodes?; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)%⊦ pre-rename-overwrite-keep-parent (parent_inode, old_dent, old_child_inode, new_dent, new_child_inode, fs, ri, ro) ↔ valid-dentry(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(parent_inode.ino, new_dent.name)} ) ∧ valid-dentry(parent_inode.ino, old_dent, fs, ri, ro) ∧ valid-dir-inode(parent_inode, fs, ri) ∧ valid-wb-inode(old_child_inode, fs, ri) ∧ old_child_inode.ino = old_dent.ino ∧ parent_inode.size ≥ 1 ∧ (old_child_inode.directory → parent_inode.nsubdirs ≥ 1); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)% ⊦ mkdentry(str, m).dentry?; (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-dir-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ valid-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri; (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ valid-wb-inode(inode, fs, ri) ↔ valid-file-inode(inode, fs, ri) ∨ valid-dir-inode(inode, fs, ri); (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-file-ino(ino, fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ {key} = ∅ ++ key; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)