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Proof step 50 from proof refine-rename-new-keep-parent (previous step)

ri = (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], fs0[ri0[inodekey(m3)]].size ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, fs0[ri0[dentrykey(m3, str)]].dentry?, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(m3)]].inode?, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(fs0[ri0[dentrykey(m3, str)]].ino) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m3) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m3, str)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m3)]].size, ¬ dentrykey(m3, str0) ∈ ri0, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ ri0 -- dentrykey(m3, str), boolvar1 → 1 ≤ fs0[ri0[inodekey(m3)]].nsubdirs, boolvar3 → boolvar0, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nsubdirs ∨ fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].size, fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nlink ∧ m2 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].size ∧ m1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].directory ∧ m0 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m3, str)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1 ⊦ [aubifs_core_index_store# (inodekey(m3), adr3, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar2 ; ri); new_dent := mkdentry(str0, mkdentry(str, fs0[ri0[dentrykey(m3, str)]].ino).ino); old_dent := negdentry(mkdentry(str, fs0[ri0[dentrykey(m3, str)]].ino).name); old_parent_inode := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).size)] ( ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0)) ∧ ri-inj(ri) ∧ log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ]) ∧ m3 ≠ 0 → ⟪new_parent_inode := old_parent_inode⟫ ⟨old_dent_inode0 := mkinode(fs0[ri0[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2); new_dent_inode0 := new_dent_inode; old_dent0 := mkdentry(str, fs0[ri0[dentrykey(m3, str)]].ino); old_dent1 := negdentry(str0); old_inode := mkinode(m3, md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); old_dent_inode := mkinode(fs0[ri0[dentrykey(m3, str)]].ino, md, boolvar1, m0, m1, m2); new_inode := mkinode(m3, md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ orphans (abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri), abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(m3, str)]].ino)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri)) = abs-keys(orphans(fs0, ri0)) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), fs0[ri0[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
fs0[ri0[dentrykey(m3, str)]] = dentrynode(key, m), ri = (ri0 -- dentrykey(m3, str))[dentrykey(m3, str0), adr2], fs0[ri0[dentrykey(m3, str)]].dentry?, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(m3)]].inode?, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri0[dentrykey(m3, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m3) ∈ ri0, dentrykey(m3, str) ∈ ri0, inodekey(m) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m3)]].size, boolvar3 → boolvar0, boolvar1 → 1 ≤ fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m2 = fs0[ri0[inodekey(m)]].size ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ boolvar1 ∨ ¬ fs0[ri0[inodekey(m)]].directory ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = 0 ∧ ¬ boolvar1, ¬ fs0[ri0[inodekey(m)]].directory ∧ ¬ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∨ fs0[ri0[inodekey(m)]].directory ∧ boolvar1 ∧ m0 = fs0[ri0[inodekey(m)]].nlink ∧ m1 = fs0[ri0[inodekey(m)]].nsubdirs ∧ m2 = fs0[ri0[inodekey(m)]].size, links(m3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m3 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO ⊦ [aubifs_core_index_store# (inodekey(m3), adr3, fi, orphans(fs0, ri0), fo, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar2 ; ri); new_dent := mkdentry(str0, mkdentry(str, m).ino); old_dent := negdentry(mkdentry(str, m).name); old_parent_inode := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size).size)] ( ubifs-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ orphans-cons (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri, orphans(fs0, ri0)) ∧ ri-inj(ri) ∧ log-cons (log0, fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ]) ∧ m3 ≠ 0 → ⟪new_parent_inode := old_parent_inode⟫ ⟨old_dent_inode0 := mkinode(m, md, boolvar1, m0, m1, m2); new_dent_inode0 := new_dent_inode; old_dent0 := mkdentry(str, m); old_dent1 := negdentry(str0); old_inode := mkinode(m3, md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); old_dent_inode := mkinode(m, md, boolvar1, m0, m1, m2); new_inode := mkinode(m3, md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size); files := abs-files(fs0, ri0); dirs := abs-dirs(fs0, ri0); afs_rename#(; old_inode, new_inode, old_dent_inode, new_dent_inode, old_dent0, old_dent1, err0, dirs, files; boolvar3)⟩ ( dirs = abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ files = abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri) ∧ orphans (abs-dirs (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri), abs-files (fs0[adr1, dentrynode(dentrykey(m3, str), 0)][adr2, dentrynode(dentrykey(m3, str0), m)] [adr3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size) ], ri)) = abs-keys(orphans(fs0, ri0)) ∧ (boolvar3 → boolvar2) ∧ old_parent_inode = old_inode ∧ new_parent_inode = new_inode ∧ old_dent_inode0 = old_dent_inode ∧ new_dent_inode0 = new_dent_inode ∧ old_dent = old_dent0 ∧ new_dent = old_dent1 ∧ ESUCCESS = err0)), fs0[ri0[inodekey(m3)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, dentrykey(m3, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m3, str), fs0[ri0[inodekey(m3)]].nlink = 0 ∧ m3 ≠ ROOT_INO

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs0[ri0[dentrykey(m3, str)]], key, m]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs0[ri0[dentrykey(m3, str)]], key, m