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Proof step 67 from proof inv-rename-overwrite-keep-parent (previous step)

n0 + (boolvar3 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, m0 + 1 = fs0[ri0[inodekey(m)]].size, m8 + 1 = fs0[ri0[inodekey(m1)]].nlink, ¬ fs0[ri0[inodekey(m1)]].directory ↔ ¬ boolvar0, fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key, m1), ri = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], adr1 ≠ adr4, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr4, adr2 ≠ adr3, adr3 ≠ adr4, m ≠ 0, m1 ≠ 0, m1 ≠ ROOT_INO, mkdentry(str, m2) ≠ mkdentry(str0, m1), fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(m1)]].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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, ¬ inodekey(m) ∈ ro, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr4 ∈ fs0, ¬ adr2 ∈ ri0 -- dentrykey(m, str), fs0[ri0[inodekey(m1)]].directory → dentrykeys(inodekey(m1), ri0) = ∅, m8 = 0 → links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), ¬ boolvar0 ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m1)]].directory ∧ boolvar2 ∧ m6 = fs0[ri0[inodekey(m1)]].size, ¬ 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, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0) ] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m1), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0) ] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); nd := inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6); log := (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '; fs := fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0) ] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m1), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(str0, mkdentry(str, m2).ino); old_dent := negdentry(str); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m0).size); new_child_inode := mkinode(m1, 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 68:
m8 + 1 = fs0[ri0[inodekey(m1)]].nlink, m0 + 1 = m11, n0 + (boolvar3 ⊃ 1;0) = m7, ¬ fs0[ri0[inodekey(m1)]].directory ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str0)]] = dentrynode(key, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m)]] = inodenode(key2, md2, boolvar1, m4, m7, m11), boolvar1, ri = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], fs0[ri0[inodekey(m1)]].inode?, 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-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, m8 = 0 → links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), fs0[ri0[inodekey(m1)]].directory → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m1)]].directory ∧ boolvar2 ∧ m6 = fs0[ri0[inodekey(m1)]].size ⊦ ⟪aubifs_core_index_store# (inodekey(m), adr3, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m1), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); nd := inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6); log := (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '; fs := fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m, str0), m2)][adr3, inodenode(inodekey(m), md, true, m4, n0, m0)] [adr4, inodenode(inodekey(m1), md1, boolvar2, m8, fs0[ri0[inodekey(m1)]].nsubdirs, m6) ]; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(m1), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(str0, mkdentry(str, m2).ino); old_dent := negdentry(str); parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m4, n0, m0).meta, inodenode(inodekey(m), md, true, m4, n0, m0).directory, inodenode(inodekey(m), md, true, m4, n0, m0).nlink, inodenode(inodekey(m), md, true, m4, n0, m0).nsubdirs, inodenode(inodekey(m), md, true, m4, n0, m0).size); new_child_inode := mkinode(m1, 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, m = 0, m1 = 0, m1 = ROOT_INO, mkdentry(str, m2) = mkdentry(str0, m1), inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str)

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)]], key2, md2, boolvar0, m4, m7, m11]

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)]], key2, md2, boolvar0, m4, m7, m11