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Proof step 536 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), ri = ri0[dentrykey(m, str0), adr2], fs0[ri0[inodekey(m)]].size ≠ 0, adr1 ≠ adr4, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr4, adr2 ≠ adr3, adr3 ≠ adr4, m0 ≠ 0, m8 ≠ ROOT_INO, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m8)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m)]].size, ¬ inodekey(m) ∈ ro, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr4 ∈ fs0, ¬ adr2 ∈ ri0 -- dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ fs0[ri0[inodekey(m)]].nsubdirs, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_index_store# (inodekey(m), adr3, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m8), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); nd := inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6); log := (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '; fs := fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size) ] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m8), ri, fi, fo, fs, log, boolvar; ro); new_dent0 := mkdentry(str0, mkdentry(str0, m8).ino); old_dent := negdentry(str0); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[inodekey(m)]].size).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 537:
fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key, md2, boolvar1, m1, m2, m4), boolvar1, ri = ri0[dentrykey(m, str0), adr2], fs0[ri0[inodekey(m)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ ⟪aubifs_core_index_store# (inodekey(m), adr3, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)][adr3, inodenode(inodekey(m), md, true, m1, m2, m4)] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m8), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)][adr3, inodenode(inodekey(m), md, true, m1, m2, m4)] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); nd := inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6); log := (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '; fs := fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)][adr3, inodenode(inodekey(m), md, true, m1, m2, m4)] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m8), ri, fi, fo, fs, log, boolvar; 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)), adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m0 = 0, m4 = 0, m8 = ROOT_INO, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0)

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] → [fs0[ri0[inodekey(m)]], key, md2, boolvar0, m1, m2, m4]

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: fs0[ri0[inodekey(m)]], key, md2, boolvar0, m1, m2, m4