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Proof step 516 from proof inv-rename-overwrite-keep-parent (previous step)

key = inodekey(fs[ri[dentrykey(m, str0)]].ino), m0 = fs[ri[dentrykey(m, str0)]].ino, m1 = fs[ri[inodekey(m)]].nlink, m2 = fs[ri[inodekey(m)]].nsubdirs, m4 = fs[ri[inodekey(m)]].size, m5 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink, m7 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nsubdirs, new_dent = mkdentry(str0, fs[ri[dentrykey(m, str0)]].ino), fs[ri[dentrykey(m, str0)]].ino ≠ ROOT_INO, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, fs[ri[dentrykey(m, str0)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].inode?, ro.inodes?, fo.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(ri), ri-inj(fi), ubifs-cons(fs, ri, ro, fi, fo, log), ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)] ∈ fs, ri[dentrykey(m, str0)] ∈ fs, inodekey(m) ∈ ri, inodekey(fs[ri[dentrykey(m, str0)]].ino) ∈ ri, dentrykey(m, str0) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, ¬ inodekey(m) ∈ ro, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m, str0)]].ino), ri) = ∅, fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].nlink = 1 → links(fs[ri[dentrykey(m, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ ¬ boolvar2 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ boolvar2 ∧ m6 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].size, ¬ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ ¬ boolvar3 ∨ fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].directory ∧ boolvar3 ∧ m3 = fs[ri[inodekey(fs[ri[dentrykey(m, str0)]].ino)]].size, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_journal_add4# (dentrynode(dentrykey(m, new_dent.name), 0), dentrynode(dentrykey(m, new_dent.name), new_dent.ino), inodenode(inodekey(m), md, true, m1, m2, m4), inodenode(key, md1, boolvar2, m5, m7, m6), ri, fi, ro, fo ; adr2, adr1, adr0, adr, fs, log ; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, new_dent.name), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, new_dent.name), adr1, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(key, md1, boolvar2, m5, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar0; ro); new_dent0 := mkdentry(new_dent.name, new_dent.ino); old_dent := negdentry(new_dent.name); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m1, m2, m4).meta, inodenode(inodekey(m), md, true, m1, m2, m4).directory, inodenode(inodekey(m), md, true, m1, m2, m4).nlink, inodenode(inodekey(m), md, true, m1, m2, m4).nsubdirs, inodenode(inodekey(m), md, true, m1, m2, m4).size); new_child_inode := mkinode(m0, 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

Proof step 517:
fs[ri[dentrykey(m, str0)]] = dentrynode(key0, m8), key = inodekey(m8), m0 = m8, m1 = fs[ri[inodekey(m)]].nlink, m2 = fs[ri[inodekey(m)]].nsubdirs, m4 = fs[ri[inodekey(m)]].size, m5 = fs[ri[inodekey(m8)]].nlink, m7 = fs[ri[inodekey(m8)]].nsubdirs, new_dent = mkdentry(str0, m8), fs[ri[dentrykey(m, str0)]].dentry?, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m8)]].inode?, 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, str0) ∈ ri, inodekey(m8) ∈ ri, inodekey(m) ∈ ri, ri[dentrykey(m, str0)] ∈ fs, ri[inodekey(m8)] ∈ fs, 1 ≤ fs[ri[inodekey(m)]].size, boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, fs[ri[inodekey(m8)]].nlink = 1 → links(m8, fs, ri) = ∅ ++ dentrykey(m, str0), fs[ri[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri) = ∅, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, ¬ fs[ri[inodekey(m8)]].directory ∧ ¬ boolvar3 ∨ fs[ri[inodekey(m8)]].directory ∧ boolvar3 ∧ m3 = fs[ri[inodekey(m8)]].size, ¬ fs[ri[inodekey(m8)]].directory ∧ ¬ boolvar2 ∨ fs[ri[inodekey(m8)]].directory ∧ boolvar2 ∧ m6 = fs[ri[inodekey(m8)]].size ⊦ ⟪aubifs_core_journal_add4# (dentrynode(dentrykey(m, new_dent.name), 0), dentrynode(dentrykey(m, new_dent.name), new_dent.ino), inodenode(inodekey(m), md, true, m1, m2, m4), inodenode(key, md1, boolvar2, m5, m7, m6), ri, fi, ro, fo ; adr2, adr1, adr0, adr, fs, log ; boolvar0, err); if err = ESUCCESS then {aubifs_core_index_remove#(dentrykey(m, new_dent.name), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, new_dent.name), adr1, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(inodekey(m), adr0, fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(key, adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(key, md1, boolvar2, m5, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(key, ri, fi, fo, fs, log, boolvar0; ro); new_dent0 := mkdentry(new_dent.name, new_dent.ino); old_dent := negdentry(new_dent.name); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m1, m2, m4).meta, inodenode(inodekey(m), md, true, m1, m2, m4).directory, inodenode(inodekey(m), md, true, m1, m2, m4).nlink, inodenode(inodekey(m), md, true, m1, m2, m4).nsubdirs, inodenode(inodekey(m), md, true, m1, m2, m4).size); new_child_inode := mkinode(m0, 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[inodekey(m8)]].nlink = 0, fs[ri[inodekey(m)]].size = 0, m8 = ROOT_INO, inodekey(m) ∈ ro

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, str0)]], key0, m8]

Additional information

Used simplifier rules: ⊦ nd.dentry? → (key = nd.key ∧ m = nd.ino ↔ nd = dentrynode(key, m)); (elim) Used terms: fs[ri[dentrykey(m, str0)]], key0, m8