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Proof step 786 from proof inv-truncate (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, 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-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), datakey(ino, n) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino) ∈ ri0, buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE, ino ≠ m ∨ ¬ min(n0, m3) ≤ n * VFS_PAGE_SIZE ⊦ adr1 = ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[datakey(ino, n)], m = 0, fs0[ri0[inodekey(ino)]].directory, inodekey(m) ∈ ro, ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[datakey(ino, n)] ∈ fs0, adr1 ∈ fs0, ((ri0 \ datakeys(inodekey(m), min(n0, m3), ri0)) ⊖ ro)[datakey(ino, n)] ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro, m3 ≤ n0 ∧ m3 % VFS_PAGE_SIZE ≠ 0, 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 \ datakeys(inodekey(m), min(n0, m3), ri0), ro] flags: <all paths>

Additional information

Used simplifier rules: at-diff-ri: ⊦ (ri \ ks)[key] = (key ∈ ks ⊃ (∅)[key];ri[key]);%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (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)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ls)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: ino, n, ri0 \ datakeys(inodekey(m), min(n0, m3), ri0), ro