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Proof step 137 from proof inv-rmdir (previous step)

fs0[ri0[inodekey(m2)]] = inodenode(key1, md2, true, 1, m5, m6), fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m2), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m3, m + 1, m1 + 1), dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m0, str), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m0, str) ∈ ri0, key2 ∈ ri0, key2.data? → ¬ inodekey(key2.ino) ∈ ro, m3 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, key2 = inodekey(m2), key2 = dentrykey(m0, str), m0 = 0, m2 = ROOT_INO, m2 = 0, key2 ∈ (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3] ⊖ (ro ++ inodekey(m2)), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m2) ∈ ro, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, key2 ∈ ro

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: in-dels-ro seq: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks) subst: [key, ri, ks] → [key2, (ri0[inodekey(m0), adr1] -- dentrykey(m0, str) )[inodekey(m2), adr3 ], ro ++ inodekey(m2)] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ≠ key0 → (key ∈ ks ++ key0 ↔ key ∈ ks); (s)% ⊦ key ∈ ks ++ key0 ↔ key = key0 ∨ key ∈ ks; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s) Used terms: key2, (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3], ro ++ inodekey(m2)