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Proof step 267 from proof inv-rename-overwrite-reparent (previous step)

1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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), key ∈ ri0, ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO ⊦ (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4] ⊖ inodekey(m8))[key] = (inodekey(m0) = key ⊃ adr4;(inodekey(m) = key ⊃ adr3;(dentrykey(m0, str0) = key ⊃ adr2;ri0[key]))), adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, key = inodekey(m8), key = dentrykey(m, str), m = 0, m0 = 0, m0 = m, m5 = 0, m8 = 0, m8 = ROOT_INO, key.data?, fs0[ri0[inodekey(m8)]].directory, fs0[ri0[inodekey(m5)]].directory, key ∈ ro, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr5 ∈ log0, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3]

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-del-ro-nodata seq: ⊦ key ∈ ri ∧ key ≠ key0 ∧ ¬ key.data? → (ri ⊖ key0)[key] = ri[key] subst: [key, ri, key0] → [key, ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2] [inodekey(m), adr3 ] [inodekey(m0), adr4 ], inodekey(m8)] 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]);% ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws) Used terms: key, ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2] [inodekey(m), adr3 ] [inodekey(m0), adr4 ], inodekey(m8)