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Proof step 19 from proof refine-rename-overwrite-reparent-file (previous step)

false ↔ mkinode(m, md, false, m0, 0, m2).directory, boolvar1 ↔ false, 0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nsubdirs, 0 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nsubdirs, dirs = abs-dirs(fs, ri), err = err0, fi0 = fi, files = abs-files(fs, ri), fo0 = fo, m = fs[ri[dentrykey(m9, str)]].ino, m0 = fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].nlink, m1 = fs[ri[dentrykey(m4, str0)]].ino, m10 = fs[ri[inodekey(m9)]].nlink, m11 = fs[ri[inodekey(m9)]].nsubdirs, m12 = fs[ri[inodekey(m9)]].size, m3 = fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, m6 = fs[ri[inodekey(m4)]].nlink, m7 = fs[ri[inodekey(m4)]].nsubdirs, m8 = fs[ri[inodekey(m4)]].size, new_child_inode = mkinode(fs[ri[dentrykey(m4, str0)]].ino, md0, false, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink, 0, m5), new_dent = mkdentry(str0, fs[ri[dentrykey(m4, str0)]].ino), new_parent_inode = mkinode(m4, md1, true, fs[ri[inodekey(m4)]].nlink, fs[ri[inodekey(m4)]].nsubdirs, fs[ri[inodekey(m4)]].size), old_child_inode0 = mkinode(m, md, false, m0, 0, m2), old_dent = mkdentry(str, fs[ri[dentrykey(m9, str)]].ino), old_parent_inode = mkinode(m9, md2, true, fs[ri[inodekey(m9)]].nlink, fs[ri[inodekey(m9)]].nsubdirs, fs[ri[inodekey(m9)]].size), ro = orphans(fs, ri), fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m9)]].directory, orphans(fs, ri).inodes?, ro.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)), orphans-cons(fs, ri, ro), pre-rename-overwrite-reparent(old_parent_inode, old_dent, mkinode(m, md, false, m0, 0, m2), new_parent_inode, new_dent, new_child_inode, fs, ri, ro), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), replay-cons-strong(fs, ri, ro, fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), ubifs-cons(fs, ri, ro, fi, fo, log), inodekey(m9) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m4, str0) ∈ ri, inodekey(fs[ri[dentrykey(m4, str0)]].ino) ∈ ri, dentrykey(m9, str) ∈ ri, inodekey(fs[ri[dentrykey(m9, str)]].ino) ∈ ri, 1 ≤ fs[ri[inodekey(m9)]].size, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m4, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m4, str0), boolvar → boolvar0, fs[ri[inodekey(m4)]].nlink ≠ 0 ∨ m4 = ROOT_INO, fs[ri[inodekey(m9)]].nlink ≠ 0 ∨ m9 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m9, abs-dirs(fs, ri)) ≠ ∅ ∨ m9 = ROOT_INO ⊦ [aubifs_rename_overwrite_reparent# (false, mkinode(m, md, false, m0, 0, m2), fi, fo ; old_parent_inode, new_parent_inode, new_child_inode, old_dent, new_dent, err, ri, ro, fs, log, boolvar0)] ( ubifs-cons(fs, ri, ro, fi0, fo0, log) ∧ replay-cons-strong(fs, ri, ro, fi0, fo0, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ log-cons(log, fs) ∧ ro.inodes? → ⟨old_dent_inode0 := mkinode(m, md, false, m0, 0, m2); old_dent0 := mkdentry(str, m); old_dent1 := mkdentry(str0, m1); old_dent_inode := mkinode(m, md, false, m0, 0, m2); new_dent_inode := mkinode(m1, md0, false, m3, 0, m5); new_inode := mkinode(m4, md1, true, m6, m7, m8); old_inode := mkinode(m9, md2, true, m10, m11, m12); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (boolvar → boolvar0) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_child_inode = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ err = err0)), fs[ri[dentrykey(m4, str0)]].ino = ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].nlink = 0, fs[ri[inodekey(m9)]].size = 0, m9 = m4, fs[ri[inodekey(fs[ri[dentrykey(m4, str0)]].ino)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m9, str)]].ino)]].directory, fs[ri[inodekey(m9)]].nlink = 0 ∧ m9 ≠ ROOT_INO, fs[ri[inodekey(m4)]].nlink = 0 ∧ m4 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ 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)% ⊦ {key} = ∅ ++ key; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)% ⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-rename-overwrite-reparent (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, 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 ∧ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)