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Proof step 529 from proof refine-rename-overwrite-keep-parent-identity (previous step)

fs[ri[inodekey(m6)]] = inodenode(key0, md2, true, m7, m8, m9), fs[ri[dentrykey(m6, str)]] = dentrynode(key, m), dirs = abs-dirs(fs, ri), err = err1, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent2, new_dent_inode = mkinode(m, md, boolvar3, m0, m1, m2), new_inode = mkinode(m6, md1, true, m7, m8, m9), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent1, old_dent1 = mkdentry(str, m), old_dent2 = mkdentry(str, m), old_dent_inode = mkinode(m, md0, boolvar2, m3, m4, m5), old_inode = mkinode(m6, md1, true, m7, m8, m9), old_parent_inode = old_inode, 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)), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(m6) ∈ ri, ri[inodekey(m6)] ∈ fs, inodekey(m) ∈ ri, ri[dentrykey(m6, str)] ∈ fs, dentrykey(m6, str) ∈ ri, 1 ≤ m9, ⌊err0⌋ , boolvar2 → 1 ≤ m8, m0 = 1 → links(m, fs, ri) = ∅ ++ dentrykey(m6, str), boolvar4 → boolvar1, fs[ri[inodekey(m)]].directory → abs-children(m, fs, ri) = ∅, fs[ri[inodekey(m)]].directory → dentrykeys(inodekey(m), ri) = ∅, m7 ≠ 0 ∨ m6 = ROOT_INO, links(m6, abs-dirs(fs, ri)) ≠ ∅ ∨ m6 = ROOT_INO, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar2 ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ m5 = fs[ri[inodekey(m)]].size, ¬ fs[ri[inodekey(m)]].directory ∧ ¬ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∨ fs[ri[inodekey(m)]].directory ∧ boolvar3 ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ m2 = fs[ri[inodekey(m)]].size, fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m5 = fs[ri[inodekey(m)]].size ∧ m4 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar2 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m3 = fs[ri[inodekey(m)]].nlink ∧ m4 = 0 ∧ ¬ boolvar2, fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m2 = fs[ri[inodekey(m)]].size ∧ m1 = fs[ri[inodekey(m)]].nsubdirs ∧ boolvar3 ∨ ¬ fs[ri[inodekey(m)]].directory ∧ m0 = fs[ri[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar3 ⊦ m = ROOT_INO, m = 0, m0 = 0, m6 = 0, m9 = 0, pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), m7 = 0 ∧ m6 ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ dir-empty(ino, dirs, files) ↔ dirs[ino].entries = ∅; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%⊦ abs-dir(ino, fs, ri) = mkdir (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, fs[ri[inodekey(ino)]].nsubdirs, abs-children(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory → abs-dirs(fs, ri)[ino] = abs-dir(ino, fs, ri); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)% ⊦ mkdentry(str, m).dentry?; (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ ¬ mkdentry(str, m).negdentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)%⊦ dentrykey(ino, str) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].directory; (ss)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-rename (old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files) ↔ ( valid-negdentry(new_parent_inode.ino, new_dent, dirs, files) ∨ valid-dentry(new_parent_inode.ino, new_dent, dirs, files) ∧ valid-wb-inode(new_child_inode, dirs, files) ∧ new_child_inode.ino = new_dent.ino ∧ ( valid-file-ino(new_dent.ino, dirs, files) ↔ valid-file-ino(old_dent.ino, dirs, files)) ∧ ( valid-dir-ino(new_dent.ino, dirs, files) → new_dent.ino ≠ ROOT_INO ∧ dir-empty(new_dent.ino, dirs, files))) ∧ valid-dentry(old_parent_inode.ino, old_dent, dirs, files) ∧ valid-dir-inode(old_parent_inode, dirs, files) ∧ valid-dir-inode(new_parent_inode, dirs, files) ∧ ( new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta) ∧ valid-wb-inode(old_child_inode, dirs, files) ∧ old_child_inode.ino = old_dent.ino; (s)