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Proof step 376 from proof inv-truncate (previous step)

m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key, md, boolvar, m, m1, m2), ¬ boolvar, replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ 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), 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, 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, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) ∧ ¬ adr3 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ⊃ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 377:
m = 0 ∧ m0 ≠ ROOT_INO ↔ inodekey(m0) ∈ ro, VFS_PAGE_SIZE = n0 + m4 % VFS_PAGE_SIZE, fs0[ri0[datakey(m0, m4 / VFS_PAGE_SIZE)]] = datanode(datakey(m0, m4 / VFS_PAGE_SIZE), buf0), fs0[ri0[inodekey(m0)]] = inodenode(key, md, false, m, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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, 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, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) ∧ ¬ adr3 ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ∧ ( inodekey(m0) ∈ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) ⊃ (m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m0) ) [datakey(m0, m4 / VFS_PAGE_SIZE), adr3 ] ;(m ≠ 0 ∨ m0 = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, m, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m0), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m0), m4, replay-log (log0, fs0[adr1, truncnode(inodekey(m0), m4)][adr2, inodenode(inodekey(m0), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m0, m4 / VFS_PAGE_SIZE), fill(buf0, zero, m4 % VFS_PAGE_SIZE, n0)) ], 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

Additional information

Used simplifier rules: ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s)