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Proof step 95 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, m0 = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, buf-opt.some?, 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m) ) ) = ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro ∧ ¬ adr3 ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo))) ⊖ inodekey(m) ) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo) ∧ replay-safe (log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)] [adr3, datanode(datakey(m, m3 / VFS_PAGE_SIZE), fill(buf-opt.buf, zero, m3 % VFS_PAGE_SIZE, n0)) ], fi ⊖ fo)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
# buf-opt.buf = VFS_PAGE_SIZE, m0 = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, ro.inodes?, fo.inodes?, buf-opt.some?, 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( inodekey(m) ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo))) ⊖ inodekey(m) ) ⊃ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo))) ⊖ inodekey(m) ) [datakey(m, m3 / VFS_PAGE_SIZE), adr3 ] ;(m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo))) ⊖ inodekey(m) ) ) = ( ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2] \ datakeys(inodekey(m), m3, ri0[datakey(m, m3 / VFS_PAGE_SIZE), adr3][inodekey(m), adr2])) ⊖ ro ∧ ¬ adr3 ∈ (m0 ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, 0, m1, n1)], fi ⊖ fo))) ⊖ inodekey(m) ) ∧ ¬ adr2 ∈ replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) \ datakeys (inodekey(m), m3, replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)) ∧ ¬ adr1 ∈ replay-log(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo) ∧ replay-safe(log0, fs0[adr1, truncnode(inodekey(m), m3)][adr2, inodenode(inodekey(m), md0, false, m0, m1, n1)], fi ⊖ fo)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ log → (replay-safe(log, fs[adr, nd], ri) ↔ replay-safe(log, fs, ri)); (s)%⊦ ¬ adr ∈ log → replay-log(log, fs[adr, nd], ri) = replay-log(log, fs, ri); (s)