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Proof step 691 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m)]] = inodenode(key, md, true, m1, m2, m4), 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), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), adr2 ∈ ri0 -- dentrykey(m, str0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m8)] ∈ fs0, 1 ≤ m4, boolvar3 → 1 ≤ m2, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m1 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m0 = 0, m4 = 0, m8 = ROOT_INO, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [adr, ri] → [adr2, ri0 -- dentrykey(m, str0)] flags: <all paths>

Additional information

Used simplifier rules: at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss) Used terms: adr2, ri0 -- dentrykey(m, str0)