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Proof step 618 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(key2, md2, true, m1, m2, m4), 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), 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 ⊦ (ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] = ri0[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] ⊖ ro, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m0 = 0, m4 = 0, m8 = ROOT_INO, m8 = 0, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str0)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 619:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 620:
fs0[ri0[inodekey(m)]] = inodenode(key2, md2, true, m1, m2, m4), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key0, m8), fs0[ri0[inodekey(m8)]] = inodenode(key1, md0, boolvar0, m0, m9, m10), 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m8)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m4, boolvar0 → dentrykeys(inodekey(m8), ri0) = ∅, m0 = 1 → links(m8, fs0, ri0) = ∅ ++ dentrykey(m, str0), boolvar3 → 1 ≤ m2, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m1 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m0 = 0, m4 = 0, m8 = 0, m8 = ROOT_INO, adr2 ∈ ri0 -- dentrykey(m, str0), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr4 ∈ log0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, ∀ key. ( key ∈ (ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] ↔ key ∈ ri0[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] ⊖ ro) ∧ ( key ∈ (ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] → (ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4][key] = (ri0[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] ⊖ ro)[key])

Rule argument

spec: store, inst: node-index name: k-Extension seq: ⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key])) subst: [ri, ri0] → [(ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3] [inodekey(m8), adr4 ], ri0[dentrykey(m, str0), adr2][inodekey(m), adr3] [inodekey(m8), adr4 ] ⊖ ro] flags: <all paths>

Additional information

Used terms: (ri0 ⊖ ro)[dentrykey(m, str0), adr2][inodekey(m), adr3] [inodekey(m8), adr4 ], ri0[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m8), adr4] ⊖ ro