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Proof step 34 from proof inv-link (previous step)

fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, ri = ri0[inodekey(m3), adr1], fs0[ri0[dentrykey(ino0, str)]].ino ≠ 0, adr1 ≠ adr3, adr1 ≠ adr2, adr2 ≠ adr3, m3 ≠ 0, fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino)]].directory, 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), dentrykey(ino0, str) ∈ ri0, inodekey(m3) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, inodekey(ino0) ∈ ri0, inodekey(ino) ∈ ri0, ¬ fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, ¬ inodekey(ino0) ∈ ro, ¬ inodekey(m3) ∈ ro, ¬ dentrykey(m3, str0) ∈ ri0, ¬ inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, ¬ inodekey(ino) ∈ ro, ¬ adr1 ∈ fs0, ¬ adr2 ∈ fs0, ¬ adr3 ∈ fs0, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ ⟪aubifs_core_index_store# (dentrykey(m3, str0), adr2, fi, ro, fo, fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); aubifs_core_index_store# (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3, fi, ro, fo, fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); new_dent := mkdentry(str0, fs0[ri0[dentrykey(ino0, str)]].ino); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).size); c_inode0 := mkinode (fs0[ri0[dentrykey(ino0, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .meta, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .directory, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .size)⟫ ( ubifs-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri) ∧ orphans-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 35:
fs0[ri0[dentrykey(ino, str)]].ino = fs0[ri0[dentrykey(ino0, str)]].ino, adr = adr2, fs = fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], key = dentrykey(m3, str0), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri0[inodekey(m3), adr1], fs0[ri0[dentrykey(ino0, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(m3)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].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), ri0[inodekey(m3)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ri0, inodekey(m3) ∈ ri0, dentrykey(ino0, str) ∈ ri0, fs0[ri0[inodekey(m3)]].trunc? ∨ fs0[ri0[inodekey(m3)]].inode?, fs0[ri0[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO, fs0[ri0[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; aubifs_core_index_store# (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), adr3, fi, ro, fo, fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); new_dent := mkdentry(str0, fs0[ri0[dentrykey(ino0, str)]].ino); p_inode0 := mkinode (m3, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).meta, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).directory, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nlink, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).nsubdirs, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1).size); c_inode0 := mkinode (fs0[ri0[dentrykey(ino0, str)]].ino, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .meta, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .directory, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nlink, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) .size)⟫ ( ubifs-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ replay-cons-strong (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro, fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 ') ∧ file-node-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri) ∧ orphans-cons (fs0[adr1, inodenode(inodekey(m3), md0, true, fs0[ri0[inodekey(m3)]].nlink, fs0[ri0[inodekey(m3)]].nsubdirs, fs0[ri0[inodekey(m3)]].size + 1)] [adr2, dentrynode(dentrykey(m3, str0), fs0[ri0[dentrykey(ino0, str)]].ino) ] [adr3, inodenode (inodekey(fs0[ri0[dentrykey(ino0, str)]].ino), md, false, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nlink + 1, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].nsubdirs, m2) ], ri, ro)), fs0[ri0[dentrykey(ino0, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m3 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(ino0, str)]].ino)]].directory, inodekey(ino0) ∈ ro, inodekey(m3) ∈ ro, dentrykey(m3, str0) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino0, str)]].ino) ∈ ro, inodekey(ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

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?;%dentry-ubifs-cons: ⊦ dentrykey(ino, str) ∈ ri ∧ ri[dentrykey(ino, str)] ∈ fs ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → fs[ri[dentrykey(ino, str)]].dentry?;%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 ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)