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Proof step 36 from proof inv-unlink (previous step)

m3 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, fs = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], key = dentrykey(m1, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1 -- key, ri1 = ri0[inodekey(m1), adr1], fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].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(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, dentrykey(m1, str) ∈ ri0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].size ≥ 1, m3 = 0 → links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO, fs0[ri0[inodekey(m1)]].trunc? ∨ fs0[ri0[inodekey(m1)]].inode? ⊦ ⟪aubifs_core_index_store# (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), adr3, fi, ro, fo, fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], ((log0 + adr1 ') + adr2 ') + adr3 ', boolvar ; ri); log := ((log0 + adr1 ') + adr2 ') + adr3 '; m := fs0[ri0[dentrykey(m1, str)]].ino; fs := fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ]; if m3 = 0 then aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs, log, boolvar; ro); dent := negdentry(str); p_inode := mkinode (m1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).meta, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).directory, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).nlink, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).nsubdirs, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).meta, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .directory, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).nlink, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).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[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 37:
m3 + 1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, adr = adr3, fs = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], fs1 = fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ], key = inodekey(fs0[ri0[dentrykey(m1, str)]].ino), key0 = dentrykey(m1, str), log = ((log0 + adr1 ') + adr2 ') + adr3 ', log1 = ((log0 + adr1 ') + adr2 ') + adr3 ', ri = ri1 -- key0, ri1 = ri0[inodekey(m1), adr1], fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, 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[dentrykey(m1, str)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, dentrykey(m1, str) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m1)]].size, fs0[ri0[inodekey(m1)]].size ≥ 1, m3 = 0 → links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[inodekey(m1)]].trunc? ∨ fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ ⟪if ¬ adr ∈ ri ∧ adr ∈ fs ∧ key-cons(key, fs[adr]) then ri[key] := adr else abort; log1 := ((log0 + adr1 ') + adr2 ') + adr3 '; m := fs0[ri0[dentrykey(m1, str)]].ino; fs1 := fs0[adr1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1)] [adr2, dentrynode(dentrykey(m1, str), 0) ] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ]; if m3 = 0 then aubifs_core_orphans_insert#(inodekey(m), ri, fi, fo, fs1, log1, boolvar; ro); dent := negdentry(str); p_inode := mkinode (m1, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).meta, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).directory, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).nlink, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).nsubdirs, inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1).size); c_inode0 := mkinode (m, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).meta, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .directory, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).nlink, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) .nsubdirs, inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, m3, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2).size)⟫ (ubifs-cons(fs1, ri, ro, fi, fo, log1) ∧ replay-cons-strong(fs1, ri, ro, fi, fo, log1) ∧ file-node-cons(fs1, ri) ∧ orphans-cons(fs1, ri, ro)), fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, inodekey(m1) ∈ ro, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: 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?;%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 };% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)