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Proof step 1460 from proof refine-rename-overwrite-reparent-dir (previous step)

fs[ri[inodekey(m0)]] = inodenode(key4, md6, true, m14 + 1, m10, m12), fs[ri[inodekey(m11)]] = inodenode(key2, md4, true, m4, m16 + 1, m13 + 1), fs[ri[dentrykey(m7, str0)]] = dentrynode(key0, m0), fs[ri[dentrykey(m11, str)]] = dentrynode(key, m), fs[ri[inodekey(m)]] = inodenode(key1, md3, true, m1, m2, m3), fs[ri[inodekey(m7)]] = inodenode(key3, md5, true, m5, m6, m8), abs-children(m0, fs, ri) = ∅, dentrykeys(inodekey(m0), ri) = ∅, dirs = abs-dirs(fs, ri), err = err1, files = abs-files(fs, ri), new_child_inode = new_dent_inode, new_dent = old_dent1, new_dent_inode = mkinode(m0, md0, true, m14 + 1, m10, m12), new_inode = mkinode(m7, md1, true, m5, m6, m8), new_parent_inode = new_inode, old_child_inode = old_dent_inode, old_dent = old_dent0, old_dent0 = mkdentry(str, m), old_dent1 = mkdentry(str0, m0), old_dent_inode = mkinode(m, md, true, m1, m2, m3), old_inode = mkinode(m11, md2, true, m4, m16 + 1, m13 + 1), 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), dentrykey(m11, str) ∈ ri, ri[dentrykey(m11, str)] ∈ fs, inodekey(m11) ∈ ri, ri[inodekey(m11)] ∈ fs, dentrykey(m7, str0) ∈ ri, ri[dentrykey(m7, str0)] ∈ fs, ri[inodekey(m0)] ∈ fs, inodekey(m0) ∈ ri, ri[inodekey(m7)] ∈ fs, inodekey(m7) ∈ ri, ri[inodekey(m)] ∈ fs, inodekey(m) ∈ ri, ⌊err0⌋ , m14 = 0 → links(m0, fs, ri) = ∅ ++ dentrykey(m7, str0), boolvar2 → boolvar0, links(m7, abs-dirs(fs, ri)) ≠ ∅ ∨ m7 = ROOT_INO, links(m11, abs-dirs(fs, ri)) ≠ ∅ ∨ m11 = ROOT_INO, m5 ≠ 0 ∨ m7 = ROOT_INO, m4 ≠ 0 ∨ m11 = ROOT_INO ⊦ m0 = 0, m0 = ROOT_INO, m11 = 0, m11 = m7, m7 = 0, pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs, files), m4 = 0 ∧ m11 ≠ ROOT_INO, m5 = 0 ∧ m7 ≠ 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)