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Proof step 51 from proof inv-rename-overwrite-reparent (previous step)

n0 + (boolvar3 ⊃ 1;0) = fs0[ri[inodekey(m)]].nsubdirs, m1 + 1 = fs0[ri[inodekey(m)]].size, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs0[ri[inodekey(m5)]].directory, fs0[ri[dentrykey(m, str)]] = dentrynode(key, m5), adr6 = adr9, adr7 = adr10, adr8 = adr11, err = ESUCCESS, fs = fs0[adr1, nd3][adr2, nd2][adr3, nd1][adr4, nd0][adr5, nd], log = ((((log0 + adr1) + adr2) + adr3) + adr4) + adr5, m10 = fs0[ri[dentrykey(m0, str0)]].ino, m8 = fs0[ri[inodekey(m)]].nlink, nd = inodenode(inodekey(new_dent.ino), md2, boolvar1, m11, m6, m7), nd0 = inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, fs0[ri[inodekey(m0)]].size), nd1 = inodenode(inodekey(m), md, true, m8, n0, m1), nd2 = dentrynode(dentrykey(m0, new_dent.name), mkdentry(str, m5).ino), nd3 = dentrynode(dentrykey(m, str), 0), new_dent = mkdentry(str0, fs0[ri[dentrykey(m0, str0)]].ino), new_dent.dentry?, mkdentry(str, m5).dentry?, fs0[ri[inodekey(m0)]].directory, fs0[ri[inodekey(m)]].directory, fs0[ri[inodekey(m0)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri), log-cons(log0, fs0), new(adr1 ' + adr2 ' + adr3 ' + (adr4 ' + adr5), fs0), node-cons(nd3.key, nd3), node-cons(nd2.key, nd2), node-cons(nd1.key, nd1), node-cons(nd0.key, nd0), node-cons(nd.key, nd), orphans-cons(fs0, ri, ro), replay-cons-strong(fs0, ri, ro, fi, fo, log0), ri-cons(ri, fs0), ri-inj(ri), ri-inj(fi), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri, inodekey(m) ∈ ri, inodekey(fs0[ri[dentrykey(m0, str0)]].ino) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(m5) ∈ ri, dentrykey(m, str) ∈ ri, ri[inodekey(m0)] ∈ fs0, fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs0[ri[dentrykey(m0, str0)]].ino), ri) = ∅, m11 = 0 → links(fs0[ri[dentrykey(m0, str0)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str0), ¬ fs0[ri[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].size, ¬ fs0[ri[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri[inodekey(m5)]].nlink ∧ m3 = fs0[ri[inodekey(m5)]].nsubdirs ∨ fs0[ri[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri[inodekey(m5)]].nlink ∧ m3 = fs0[ri[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri[inodekey(m5)]].size, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri[inodekey(m0)]].trunc? ∨ fs0[ri[inodekey(m0)]].inode? ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(dentrykey(m0, new_dent.name), 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(m0), adr4, fi, ro, fo, fs, log, boolvar; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr5, fi, ro, fo, fs, log, boolvar; ri); nd := inodenode(inodekey(new_dent.ino), md2, boolvar1, m11, m6, m7); if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(new_dent.name, mkdentry(str, m5).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m8, n0, m1).meta, inodenode(inodekey(m), md, true, m8, n0, m1).directory, inodenode(inodekey(m), md, true, m8, n0, m1).nlink, inodenode(inodekey(m), md, true, m8, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m8, n0, m1).size); new_child_inode := mkinode(m10, 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[dentrykey(m0, str0)]].ino = ROOT_INO, m0 = m, dups(adr1 ' + adr2 ' + adr3 ' + adr4 ' + adr5 '), inodekey(m0) ∈ ro, inodekey(m) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
m1 + 1 = fs0[ri[inodekey(m)]].size, n0 + (boolvar3 ⊃ 1;0) = fs0[ri[inodekey(m)]].nsubdirs, ¬ fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory ↔ ¬ fs0[ri[inodekey(m5)]].directory, fs0[ri[dentrykey(m, str)]] = dentrynode(key, m5), fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, fs0[ri[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode(inodekey(m0), md0, true, fs0[ri[inodekey(m0)]].nlink, fs0[ri[inodekey(m0)]].nsubdirs, fs0[ri[inodekey(m0)]].size) ] [adr5, inodenode(inodekey(fs0[ri[dentrykey(m0, str0)]].ino), md2, boolvar1, m11, m6, m7) ], m10 = fs0[ri[dentrykey(m0, str0)]].ino, m8 = fs0[ri[inodekey(m)]].nlink, new_dent = mkdentry(str0, fs0[ri[dentrykey(m0, str0)]].ino), fs0[ri[dentrykey(m0, str0)]].ino ≠ ROOT_INO, fs0[ri[dentrykey(m0, str0)]].ino ≠ 0, adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr1 ≠ adr5, adr2 ≠ adr3, adr2 ≠ adr4, adr2 ≠ adr5, adr3 ≠ adr4, adr3 ≠ adr5, adr4 ≠ adr5, m ≠ 0, m0 ≠ m, m0 ≠ 0, fs0[ri[inodekey(m)]].directory, fs0[ri[inodekey(m0)]].directory, fs0[ri[inodekey(m0)]].inode?, 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-cons(ri, fs0), ri-inj(fi), ri-inj(ri), ubifs-cons(fs0, ri, ro, fi, fo, log0), ri[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri, inodekey(m5) ∈ ri, dentrykey(m0, str0) ∈ ri, inodekey(fs0[ri[dentrykey(m0, str0)]].ino) ∈ ri, inodekey(m) ∈ ri, inodekey(m0) ∈ ri, ri[dentrykey(m, str)] ∈ fs0, ¬ adr5 ∈ fs0, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m) ∈ ro, ¬ inodekey(m0) ∈ ro, m11 = 0 → links(fs0[ri[dentrykey(m0, str0)]].ino, fs0, ri) = ∅ ++ dentrykey(m0, str0), fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory → dentrykeys(inodekey(fs0[ri[dentrykey(m0, str0)]].ino), ri) = ∅, fs0[ri[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ fs0[ri[inodekey(m5)]].directory ∧ ¬ boolvar3 ∧ m2 = fs0[ri[inodekey(m5)]].nlink ∧ m3 = fs0[ri[inodekey(m5)]].nsubdirs ∨ fs0[ri[inodekey(m5)]].directory ∧ boolvar3 ∧ m2 = fs0[ri[inodekey(m5)]].nlink ∧ m3 = fs0[ri[inodekey(m5)]].nsubdirs ∧ m4 = fs0[ri[inodekey(m5)]].size, ¬ fs0[ri[inodekey(m5)]].directory ∧ ¬ boolvar1 ∧ m11 + 1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∨ fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].directory ∧ boolvar1 ∧ m11 + 1 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nlink ∧ m6 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].nsubdirs ∧ m7 = fs0[ri[inodekey(fs0[ri[dentrykey(m0, str0)]].ino)]].size ⊦ ⟪aubifs_core_index_remove#(dentrykey(m, str), fi, ro, fo, fs, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar; ri); aubifs_core_index_store# (dentrykey(m0, new_dent.name), adr2, fi, ro, fo, fs, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar; ri); aubifs_core_index_store#(inodekey(m), adr3, fi, ro, fo, fs, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar; ri); aubifs_core_index_store#(inodekey(m0), adr4, fi, ro, fo, fs, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar; ri); aubifs_core_index_store#(inodekey(new_dent.ino), adr5, fi, ro, fo, fs, ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 ', boolvar; ri); nd := inodenode(inodekey(new_dent.ino), md2, boolvar1, m11, m6, m7); log := ((((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') + adr5 '; if nd.nlink = 0 then aubifs_core_orphans_insert#(inodekey(new_dent.ino), ri, fi, fo, fs, log, boolvar; ro); new_dent := mkdentry(new_dent.name, mkdentry(str, m5).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, m8, n0, m1).meta, inodenode(inodekey(m), md, true, m8, n0, m1).directory, inodenode(inodekey(m), md, true, m8, n0, m1).nlink, inodenode(inodekey(m), md, true, m8, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, m8, n0, m1).size); new_child_inode := mkinode(m10, 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)% ⊦ 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)% ⊦ dentrykey(m, str).dentry?; (s)% ⊦ node-cons(key0, dentrynode(key1, ino)) ↔ key0.dentry?; (s)% ⊦ dentrynode(key, m).key = key; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).name = str; (s)