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Proof step 767 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri0[inodekey(m)]].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), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ adr1 = adr2, m = 0, fs0[ri0[inodekey(m)]].directory, adr1 ∈ fs0, adr2 ∈ fs0, m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0, replay-safe (log0 + adr1 ' + adr2 ', fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) ∧ replay (log0 + adr1 ' + adr2 ', fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi, fo) = (ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m3), ri0[inodekey(m), adr2])) ⊖ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 768:
fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ inodekey(m) ∈ ro, fs0[ri0[inodekey(m)]].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(m)] ∈ fs0, inodekey(m) ∈ ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE ⊦ adr1 = adr2, m = 0, fs0[ri0[inodekey(m)]].directory, adr2 ∈ fs0, adr1 ∈ fs0, m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0, replay-safe (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m), min(n0, m3), replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo)) ∧ (fs0[ri0[inodekey(m)]].nlink ≠ 0 ∨ m = ROOT_INO ⊃ ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m), min(n0, m3), replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo)) )[inodekey(m), adr2 ] ; ( replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo) \ datakeys (inodekey(m), min(n0, m3), replay-log (log0, fs0[adr1, truncnode(inodekey(m), min(n0, m3))] [adr2, inodenode(inodekey(m), md0, false, fs0[ri0[inodekey(m)]].nlink, fs0[ri0[inodekey(m)]].nsubdirs, n0) ], fi ⊖ fo))) ⊖ inodekey(m) ) = (ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m3), ri0[inodekey(m), adr2])) ⊖ ro

Rule argument

Additional information

Used simplifier rules: at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);%⊦ replay-one(adr, inodenode(key, md, boolvar, n, n0, m), ri) = (n ≠ 0 ∨ key.ino = ROOT_INO ⊃ ri[key, adr] ;(boolvar ⊃ ri -- key;ri ⊖ key) ); (s)% ⊦ replay-log(adr ', fs, ri) = replay-one(adr, fs[adr], ri); (s)%⊦ replay-log(adr ' + log, fs, ri) = replay-log(log, fs, replay-one(adr, fs[adr], ri)); (s)% ⊦ replay(log, fs, fi, fo) = replay-log(log, fs, fi ⊖ fo); (s)%⊦ replay(ax0 + ax1, fs, fi, fo) = replay-log(ax1, fs, replay(ax0, fs, fi, fo)); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ inodekey(m).ino = m; (s)%⊦ node-cons(key0, inodenode(key1, md, boolvar, n, n0, m)) ↔ key0.inode? ∧ key0.ino ≠ 0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)%⊦ replay-safe(adr ', fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]); (s)% ⊦ replay-one(adr, truncnode(key, n), ri) = ri \ datakeys(key, n, ri); (s)% ⊦ inodekey(m).inode?; (s)% ⊦ node-cons(key0, truncnode(key1, n)) ↔ key0.inode?; (s)% ⊦ truncnode(key, m).key = key; (s)% ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ adr ≠ adr0 → (adr ∈ fs[adr0, nd] ↔ adr ∈ fs); (s)%⊦ replay-safe(adr ' + log, fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]) ∧ replay-safe(log, fs, replay-one(adr, fs[adr], ri)); (s)%⊦ replay-safe(log0 + log1, fs, ri) ↔ replay-safe(log0, fs, ri) ∧ replay-safe(log1, fs, replay-log(log0, fs, ri)); (s)