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Proof step 528 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri[inodekey(m8)]] = inodenode(key, md0, boolvar0, m0, m9, m10), adr5 = adr7, adr6 = adr8, err = ESUCCESS, fs = fs0[adr1, nd2][adr2, nd1][adr3, nd0][adr4, nd], log = (((log0 + adr1) + adr2) + adr3) + adr4, m1 = fs0[ri[inodekey(m)]].nlink, m2 = fs0[ri[inodekey(m)]].nsubdirs, m4 = fs0[ri[inodekey(m)]].size, nd = inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6), nd0 = inodenode(inodekey(m), md, true, m1, m2, m4), nd1 = dentrynode(dentrykey(m, str0), mkdentry(str0, m8).ino), nd2 = dentrynode(dentrykey(m, str0), 0), mkdentry(str0, m8).dentry?, fs0[ri[inodekey(m)]].directory, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ' + (adr3 ' + adr4), fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m8)] ∈ fs0, ri[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri, inodekey(m8) ∈ ri, dentrykey(m, str0) ∈ ri, 1 ≤ fs0[ri[inodekey(m)]].size, boolvar0 → dentrykeys(inodekey(m8), ri) = ∅, m0 = 1 → links(m8, fs0, ri) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ fs0[ri[inodekey(m)]].nsubdirs, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str0), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(m8), adr4, fi, ro, fo, fs, log, boolvar; ri); nd := 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)), fs0[ri[inodekey(m)]].size = 0, m0 = 0, m8 = ROOT_INO, dups(adr1 ' + adr2 ' + adr3 ' + adr4 '), inodekey(m) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 529:
fs0[ri[inodekey(m8)]] = inodenode(key, md0, boolvar0, m0, m9, m10), fs0[ri[dentrykey(m, str0)]] = dentrynode(key0, m8), fs = fs0[adr1, dentrynode(dentrykey(m, str0), 0)][adr2, dentrynode(dentrykey(m, str0), m8)] [adr3, inodenode(inodekey(m), md, true, fs0[ri[inodekey(m)]].nlink, fs0[ri[inodekey(m)]].nsubdirs, fs0[ri[inodekey(m)]].size) ] [adr4, inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6) ], m1 = fs0[ri[inodekey(m)]].nlink, m2 = fs0[ri[inodekey(m)]].nsubdirs, m4 = fs0[ri[inodekey(m)]].size, fs0[ri[inodekey(m)]].size ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m0 ≠ 0, m8 ≠ ROOT_INO, fs0[ri[inodekey(m)]].directory, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), dentrykey(m, str0) ∈ ri, inodekey(m8) ∈ ri, inodekey(m) ∈ ri, ri[dentrykey(m, str0)] ∈ fs0, ri[inodekey(m8)] ∈ fs0, 1 ≤ fs0[ri[inodekey(m)]].size, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m) ∈ ro, boolvar3 → 1 ≤ fs0[ri[inodekey(m)]].nsubdirs, m0 = 1 → links(m8, fs0, ri) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri) = ∅, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str0), fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(dentrykey(m, str0), adr2, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); aubifs_core_index_store#(inodekey(m8), adr4, fi, ro, fo, fs, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar; ri); nd := inodenode(inodekey(m8), md1, boolvar2, m0, m9, m6); log := (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 '; 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))

Rule argument

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ dups(adr ' + ax) ↔ dups(ax) ∨ adr ∈ ax; (ws)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)% ⊦ mkdentry(str, m).ino = m; (s)