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Proof step 26 from proof inv-rename-overwrite-reparent (previous step)

boolvar0 ↔ boolvar3, boolvar ↔ boolvar2, ¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, boolvar0 ↔ old_child_inode.directory, new_child_inode = mkinode(fs[ri[dentrykey(m0, str0)]].ino, md2, boolvar1, m5, m6, m7), new_dent = mkdentry(str0, fs[ri[dentrykey(m0, str0)]].ino), new_parent_inode = mkinode(m0, md0, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), old_child_inode = mkinode(fs[ri[dentrykey(m, str)]].ino, md1, boolvar3, m2, m3, m4), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), old_parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), old_dent.dentry?, fs[ri[dentrykey(m, str)]].dentry?, fs[ri[inodekey(m0)]].directory, fs[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rename-overwrite-reparent(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(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[dentrykey(m, str)] ∈ fs, inodekey(m0) ∈ ri, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m0, str0)]].ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m, str) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, old_parent_inode.nsubdirs ≥ (boolvar0 ⊃ 1;0), old_parent_inode.size ≥ 1, fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m0, str0)]].ino), ri) = ∅, m5 = 1 → links(fs[ri[dentrykey(m0, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪key := inodekey(new_dent.ino); nd := inodenode(key, new_child_inode.meta, new_child_inode.directory, new_child_inode.nlink - 1, new_child_inode.nsubdirs, new_child_inode.size); aubifs_core_journal_add5# (dentrynode(dentrykey(old_parent_inode.ino, old_dent.name), 0), dentrynode(dentrykey(new_parent_inode.ino, new_dent.name), old_dent.ino), inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1), inodenode (inodekey(new_parent_inode.ino), new_parent_inode.meta, new_parent_inode.directory, new_parent_inode.nlink, new_parent_inode.nsubdirs, new_parent_inode.size), nd, ri, fi, ro, fo ; adr3, adr2, adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(old_parent_inode.ino, old_dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(new_parent_inode.ino, new_dent.name), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(old_parent_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_parent_inode.ino), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar; ri); if nd.nlink = 0 then aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode0 := mkinode (old_parent_inode.ino, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .meta, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .directory, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .nlink, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .nsubdirs, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .size); new_child_inode := mkinode(new_child_inode.ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}⟫ (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)), fs[ri[dentrykey(m0, str0)]].ino = ROOT_INO, fs[ri[inodekey(m)]].size = 0, m0 = m, m5 = 0, inodekey(m0) ∈ ro, inodekey(m) ∈ ro

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 27:
boolvar0 ↔ old_child_inode.directory, ¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, boolvar ↔ boolvar2, boolvar0 ↔ boolvar3, new_child_inode = mkinode(fs[ri[dentrykey(m0, str0)]].ino, md2, boolvar1, m5, m6, m7), new_dent = mkdentry(str0, fs[ri[dentrykey(m0, str0)]].ino), new_parent_inode = mkinode(m0, md0, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), old_child_inode = mkinode(fs[ri[dentrykey(m, str)]].ino, md1, boolvar3, m2, m3, m4), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), old_parent_inode = mkinode(m, md, true, fs[ri[inodekey(m)]].nlink, fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m)]].size), new_dent.dentry?, fs[ri[dentrykey(m, str)]].dentry?, old_dent.dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m0)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs, ri), log-cons(log, fs), orphans-cons(fs, ri, ro), pre-rename-overwrite-reparent(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), dentrykey(m, str) ∈ ri, inodekey(fs[ri[dentrykey(m, str)]].ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs[ri[dentrykey(m0, str0)]].ino) ∈ ri, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs, 1 ≤ fs[ri[inodekey(m)]].size, old_parent_inode.size ≥ 1, old_parent_inode.nsubdirs ≥ (boolvar0 ⊃ 1;0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, m5 = 1 → links(fs[ri[dentrykey(m0, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m0, str0), fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m0, str0)]].ino), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ boolvar3 ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nlink ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].nsubdirs ∧ m4 = fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m5 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].size ⊦ ⟪nd := inodenode (inodekey(new_dent.ino), new_child_inode.meta, new_child_inode.directory, new_child_inode.nlink - 1, new_child_inode.nsubdirs, new_child_inode.size); aubifs_core_journal_add5# (dentrynode(dentrykey(old_parent_inode.ino, old_dent.name), 0), dentrynode(dentrykey(new_parent_inode.ino, new_dent.name), old_dent.ino), inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1), inodenode (inodekey(new_parent_inode.ino), new_parent_inode.meta, new_parent_inode.directory, new_parent_inode.nlink, new_parent_inode.nsubdirs, new_parent_inode.size), nd, ri, fi, ro, fo ; adr3, adr2, adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(old_parent_inode.ino, old_dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(new_parent_inode.ino, new_dent.name), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(old_parent_inode.ino), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_parent_inode.ino), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr, fi, ro, fo, fs, log, boolvar; ri); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(new_dent.name, old_dent.ino); old_dent := negdentry(old_dent.name); old_parent_inode0 := mkinode (old_parent_inode.ino, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .meta, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .directory, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .nlink, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .nsubdirs, inodenode (inodekey(old_parent_inode.ino), old_parent_inode.meta, old_parent_inode.directory, old_parent_inode.nlink, old_parent_inode.nsubdirs - (boolvar0 ⊃ 1;0), old_parent_inode.size - 1) .size); new_child_inode := mkinode(new_child_inode.ino, nd.meta, nd.directory, nd.nlink, nd.nsubdirs, nd.size)}⟫ (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)), fs[ri[dentrykey(m0, str0)]].ino = ROOT_INO, fs[ri[inodekey(m)]].size = 0, m0 = m, m5 = 0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro

Rule argument

Additional information

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