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Proof step 165 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, 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, datakey(ino, n) ∈ ri0, inodekey(ino) ∈ ri0, m3 ≤ n1, m0 ≠ 0 ∨ m = ROOT_INO, ino ≠ m ∨ ¬ m3 ≤ n * VFS_PAGE_SIZE ⊦ m3 % VFS_PAGE_SIZE = 0, ((ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro)[datakey(ino, n)] = ( ( 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 )[datakey(ino, n) ], adr1 = adr3, adr1 = adr2, adr2 = adr3, datakey(m, m3 / VFS_PAGE_SIZE) = datakey(ino, n), m = 0, fs0[ri0[inodekey(ino)]].directory, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(m) ∈ ro, inodekey(ino) ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [ino, n, ri, ks] → [ino, n, 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] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)% ⊦ datakeys(key, ri[inodekey(ino), adr]) = datakeys(key, ri); (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s) Used terms: ino, n, 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