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Proof step 265 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, false, 1, m11, m12), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, false, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), 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), key ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, m4 ≠ 0 ∨ m = ROOT_INO, dentrykey(m, str) = dentrykey(m, str0) ∨ key ≠ dentrykey(m, str), key = inodekey(m) ∨ key = dentrykey(m, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro ⊦ (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1))[key] = (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];ri0[key]))), adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, key = inodekey(m1), m = 0, m1 = ROOT_INO, m1 = 0, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), key.data?, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], adr4 ∈ log0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, key ∈ ro

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(m, str0), adr2] [inodekey(m), adr3 ], inodekey(m1)] 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]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);% ⊦ 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(m, str0), adr2] [inodekey(m), adr3 ], inodekey(m1)