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Proof step 283 from proof inv-unlink (previous step)

fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, false, m3 + 1, m7, m8), fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m0), fs0[ri0[inodekey(m1)]] = inodenode(key0, md1, true, m4, m5, m + 1), 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-cons-strong(fs0, ri0, ro, fi, fo, log0), 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(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, inodekey(ino) ∈ ri0, m4 ≠ 0 ∨ m1 = ROOT_INO ⊦ adr1 = adr2, adr1 = ((ri0[inodekey(m1), adr1] -- dentrykey(m1, str)) ⊖ ro)[datakey(ino, n)], adr2 = ((ri0[inodekey(m1), adr1] -- dentrykey(m1, str)) ⊖ ro)[datakey(ino, n)], m0 = ROOT_INO, m0 = 0, m1 = 0, m3 = 0, fs0[ri0[inodekey(ino)]].directory, ((ri0[inodekey(m1), adr1] -- dentrykey(m1, str)) ⊖ ro)[datakey(ino, n)] ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m1) ∈ ro, ((ri0[inodekey(m1), adr1] -- dentrykey(m1, str)) ⊖ ro)[datakey(ino, n)] ∈ log0, adr2 ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro

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[inodekey(m1), adr1] -- dentrykey(m1, str), ro] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss) Used terms: ino, n, ri0[inodekey(m1), adr1] -- dentrykey(m1, str), ro