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Proof step 172 from proof inv-unlink (previous step)

fs0[ri0[inodekey(m1)]] = inodenode(key0, md1, true, m3, m4, m + 1), fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, false, 1, m6, m7), links(m0, fs0, ri0) = ∅ ++ dentrykey(m1, 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), dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, key2 ∈ ri0, m3 ≠ 0 ∨ m1 = ROOT_INO ⊦ (ri0[inodekey(m1), adr1] ⊖ ro)[key2] = (inodekey(m1) = key2 ⊃ adr1;ri0[key2]), adr1 = adr2, adr1 = adr3, adr2 = adr3, key2 = inodekey(m0), key2 = dentrykey(m1, str), m0 = ROOT_INO, m0 = 0, m1 = 0, key2.data?, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m1) ∈ ro, key2 ∈ ro

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-nodata seq: ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key] subst: [key, ri, ks] → [key2, ri0[inodekey(m1), adr1], ro] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]); Used terms: key2, ri0[inodekey(m1), adr1], ro