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Proof step 615 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, 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-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, m4 ≤ n0 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, replay-safe (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo)) ∧ (fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo))) ⊖ inodekey(m0) ) = (ri0[inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[inodekey(m0), adr2])) ⊖ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 616:
⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro
Proof step 617:
fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, replay(log0, fs0, fi, fo) = ri0 ⊖ ro, fs0[ri0[inodekey(m0)]].inode?, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n0 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, replay-safe (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo)) ∧ (fs0[ri0[inodekey(m0)]].nlink ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)] [adr2, inodenode(inodekey(m0), md0, false, fs0[ri0[inodekey(m0)]].nlink, fs0[ri0[inodekey(m0)]].nsubdirs, n0) ], fi ⊖ fo))) ⊖ inodekey(m0) ) = (ri0[inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[inodekey(m0), adr2])) ⊖ ro

Rule argument

spec: aubifs-replay name: replay-cons-strong seq: ⊦ replay-cons-strong(fs, ri, ro, fi, fo, log) ↔ replay-safe(log, fs, fi ⊖ fo) ∧ replay(log, fs, fi, fo) = ri ⊖ ro subst: [log, fo, fi, ro, ri, fs] → [log0, fo, fi, ro, ri0, fs0] flags: <all paths>

Additional information

Used terms: log0, fo, fi, ro, ri0, fs0