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Proof step 518 from proof inv-rename-overwrite-keep-parent (previous step)

fs[ri[dentrykey(m, str0)]] = dentrynode(key0, 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, fs[ri[inodekey(m8)]].nlink ≠ 0, fs[ri[inodekey(m)]].size ≠ 0, m8 ≠ ROOT_INO, 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, ¬ inodekey(m) ∈ ro, 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, str0), 0), dentrynode(dentrykey(m, str0), mkdentry(str0, m8).ino), inodenode(inodekey(m), md, true, m1, m2, m4), inodenode(inodekey(m8), 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, str0), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, str0), 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#(inodekey(m8), adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(inodekey(m8), md1, boolvar2, m5, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m8), ri, fi, fo, fs, log, boolvar0; ro); new_dent0 := mkdentry(str0, mkdentry(str0, m8).ino); old_dent := negdentry(str0); 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(m8, 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 519:
fs[ri[dentrykey(m, str0)]] = dentrynode(key0, m8), fs[ri[inodekey(m8)]] = inodenode(key, md0, boolvar, m0, m9, m10), m1 = fs[ri[inodekey(m)]].nlink, m2 = fs[ri[inodekey(m)]].nsubdirs, m4 = fs[ri[inodekey(m)]].size, m5 = m0, m7 = m9, fs[ri[inodekey(m)]].directory, fs[ri[inodekey(m8)]].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(m8)] ∈ fs, ri[dentrykey(m, str0)] ∈ fs, inodekey(m) ∈ ri, inodekey(m8) ∈ ri, dentrykey(m, str0) ∈ ri, 1 ≤ fs[ri[inodekey(m)]].size, boolvar → dentrykeys(inodekey(m8), ri) = ∅, m0 = 1 → links(m8, fs, ri) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ fs[ri[inodekey(m)]].nsubdirs, ¬ boolvar ∧ ¬ boolvar2 ∨ boolvar ∧ boolvar2 ∧ m6 = m10, ¬ boolvar ∧ ¬ boolvar3 ∨ boolvar ∧ boolvar3 ∧ m3 = m10, fs[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_journal_add4# (dentrynode(dentrykey(m, str0), 0), dentrynode(dentrykey(m, str0), mkdentry(str0, m8).ino), inodenode(inodekey(m), md, true, m1, m2, m4), inodenode(inodekey(m8), 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, str0), fi, ro, fo, fs, log, boolvar0; ri); aubifs_core_index_store#(dentrykey(m, str0), 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#(inodekey(m8), adr, fi, ro, fo, fs, log, boolvar0; ri); nd := inodenode(inodekey(m8), md1, boolvar2, m5, m7, m6); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m8), ri, fi, fo, fs, log, boolvar0; ro); new_dent0 := mkdentry(str0, mkdentry(str0, m8).ino); old_dent := negdentry(str0); 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(m8, 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(m)]].size = 0, m0 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro

Rule argument

spec: node name: elim-03 seq: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)) subst: [nd, key, md, boolvar, m, m0, m1] → [fs[ri[inodekey(m8)]], key, md0, boolvar, m0, m9, m10]

Additional information

Used simplifier rules: ⊦ nd.inode? → ( ( ( ( (key = nd.key ∧ md = nd.meta) ∧ (boolvar ↔ nd.directory)) ∧ m = nd.nlink) ∧ m0 = nd.nsubdirs) ∧ m1 = nd.size ↔ nd = inodenode(key, md, boolvar, m, m0, m1)); (elim) Used terms: fs[ri[inodekey(m8)]], key, md0, boolvar, m0, m9, m10