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Proof step 373 from proof inv-truncate (previous step)

fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data, zero, m4 % VFS_PAGE_SIZE, n0) = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf), fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, fs0[ri0[inodekey(m0)]].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), 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[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr3 ∈ ri0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo)) ∧ ¬ adr3 ∈ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ⊃ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ) = ( ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2])) ⊖ ro

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 374:
fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data:= fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0) = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf), fs0[ri0[inodekey(m0)]].nlink = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(key, buf0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]].data?, 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), replay-safe(log0, fs0, fi ⊖ fo), 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, datakey(m0, m4 / VFS_PAGE_SIZE) ∈ ri0, ri0[datakey(m0, m4 / VFS_PAGE_SIZE)] ∈ fs0, m4 ≤ n1 ⊦ m4 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, fs0[ri0[inodekey(m0)]].directory, buf-opt.some?, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr3 ∈ 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo)) ∧ ¬ adr3 ∈ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ⊃ (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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], 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, n1) ] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ) = ( ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2] \ datakeys(inodekey(m0), m4, ri0[datakey(m0, m4 / VFS_PAGE_SIZE), adr3][inodekey(m0), adr2])) ⊖ ro

Rule argument

spec: node name: elim-05 seq: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)) subst: [nd, key, buf] → [fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]], key, buf0]

Additional information

Used simplifier rules: ⊦ nd.data? → (key = nd.key ∧ buf = nd.data ↔ nd = datanode(key, buf)); (elim) Used terms: fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]], key, buf0