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Proof step 53 from proof inv-rename-new-reparent (previous step)

m1 + 1 = fs0[ri0[inodekey(m)]].size, n0 + (boolvar2 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), ri = ri0 -- dentrykey(m, str), adr1 ≠ adr2, adr1 ≠ adr3, adr1 ≠ adr4, adr2 ≠ adr3, adr2 ≠ adr4, adr3 ≠ adr4, m0 ≠ m, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m0)]].directory, 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), dentrykey(m, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m3)] ∈ fs0, inodekey(m) ∈ ri0, ¬ adr4 ∈ fs0, ¬ adr3 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr1 ∈ fs0, ¬ inodekey(m0) ∈ ro, ¬ dentrykey(m0, str0) ∈ ri0, ¬ inodekey(m) ∈ ro, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10 ⊦ ⟪aubifs_core_index_store# (dentrykey(m0, str0), adr2, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m), adr3, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m0), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); new_dent := mkdentry(str0, mkdentry(str, m3).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).size); new_parent_inode0 := mkinode (m0, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .meta, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .directory, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .nlink, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .nsubdirs, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .size)⟫ ( ubifs-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ file-node-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri) ∧ orphans-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 54:
n0 + (boolvar2 ⊃ 1;0) = fs0[ri0[inodekey(m)]].nsubdirs, m1 + 1 = fs0[ri0[inodekey(m)]].size, fs0[ri0[inodekey(m3)]] = inodenode(key0, md1, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m3), adr = adr2, fs = fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], key = dentrykey(m0, str0), log = (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', ri = ri0 -- dentrykey(m, str), fs0[ri0[inodekey(m0)]].directory, fs0[ri0[inodekey(m)]].directory, fs0[ri0[inodekey(m)]].inode?, fs0[ri0[inodekey(m0)]].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(m)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m3)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(m, str) ∈ ri0, fs0[ri0[inodekey(m0)]].trunc? ∨ fs0[ri0[inodekey(m0)]].inode?, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m4 = m10, fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO, fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_store# (inodekey(m), adr3, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); aubifs_core_index_store# (inodekey(m0), adr4, fi, ro, fo, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ', boolvar ; ri); new_dent := mkdentry(str0, mkdentry(str, m3).ino); old_dent := negdentry(str); old_parent_inode0 := mkinode (m, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).meta, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).directory, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).nlink, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).nsubdirs, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1).size); new_parent_inode0 := mkinode (m0, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .meta, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .directory, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .nlink, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .nsubdirs, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) .size)⟫ ( ubifs-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ replay-cons-strong (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro, fi, fo, (((log0 + adr1 ') + adr2 ') + adr3 ') + adr4 ') ∧ file-node-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri) ∧ orphans-cons (fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m3)] [adr3, inodenode(inodekey(m), md, true, fs0[ri0[inodekey(m)]].nlink, n0, m1) ] [adr4, inodenode (inodekey(m0), md0, true, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs + (boolvar2 ⊃ 1;0), fs0[ri0[inodekey(m0)]].size + 1) ], ri, ro)), adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m0 = m, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, dentrykey(m0, str0) ∈ ri0, inodekey(m) ∈ ro

Rule argument

pos: right 1

Additional information

Used simplifier rules: inode-ubifs-cons: ⊦ inodekey(ino) ∈ ri ∧ ri[inodekey(ino)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[inodekey(ino)]].inode?;%aubifs_core_index_store#(KEY, ADR, FI, RO, FO, FS, LOG, CSYNCED; RI) {if ¬ ADR ∈ RI ∧ ADR ∈ FS ∧ key-cons(KEY, FS[ADR]) then RI[KEY] := ADR else abort };% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss)