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Proof step 41 from proof inv-rename-overwrite-reparent (previous step)

m1 + 1 = fs[ri[inodekey(m)]].size, n0 + (boolvar3 ⊃ 1;0) = fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(fs[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str)]].ino)]].directory, m10 = fs[ri[dentrykey(m0, str0)]].ino, m8 = fs[ri[inodekey(m)]].nlink, new_dent = mkdentry(str0, fs[ri[dentrykey(m0, str0)]].ino), old_dent = mkdentry(str, fs[ri[dentrykey(m, str)]].ino), fs[ri[dentrykey(m0, str0)]].ino ≠ ROOT_INO, m0 ≠ m, fs[ri[dentrykey(m, str)]].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), 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, ¬ inodekey(m) ∈ ro, ¬ inodekey(m0) ∈ ro, m11 = 0 → 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 ∧ m11 + 1 = 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 ∧ m11 + 1 = 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 ⊦ ⟪aubifs_core_journal_add5# (dentrynode(dentrykey(m, old_dent.name), 0), dentrynode(dentrykey(m0, new_dent.name), old_dent.ino), inodenode(inodekey(m), md, true, m8, n0, m1), inodenode(inodekey(m0), md0, true, fs[ri[inodekey(m0)]].nlink, fs[ri[inodekey(m0)]].nsubdirs, fs[ri[inodekey(m0)]].size), inodenode(inodekey(new_dent.ino), md2, boolvar1, m11, m6, m7), ri, fi, ro, fo ; adr3, adr2, adr1, adr0, adr, fs, log ; boolvar, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, old_dent.name), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m0, new_dent.name), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr1, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m0), adr0, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr, fi, ro, fo, fs, log, boolvar; ri); nd := inodenode(inodekey(new_dent.ino), md2, boolvar1, m11, m6, m7); 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 (m, inodenode(inodekey(m), md, true, m8, n0, m1).meta, inodenode(inodekey(m), md, true, m8, n0, m1).directory, inodenode(inodekey(m), md, true, m8, n0, m1).nlink, inodenode(inodekey(m), md, true, m8, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m8, n0, m1).size); new_child_inode := mkinode(m10, 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: node name: elim-02 seq: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)) subst: [nd, key, m] → [fs[ri[dentrykey(m, str)]], key, m5]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m, str)]], key, m5