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Proof step 287 from proof inv-unlink (previous step)

fs0[ri0[inodekey(m1)]] = inodenode(key0, md1, true, m4, m5, m + 1), fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m0), fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, false, m3 + 1, m7, m8), 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-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, m4 ≠ 0 ∨ m1 = ROOT_INO ⊦ ((ri0[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str))[inodekey(m0), adr3] = (ri0[inodekey(m1), adr1] -- dentrykey(m1, str))[inodekey(m0), adr3] ⊖ ro, adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, m0 = ROOT_INO, m1 = 0, m3 = 0, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, inodekey(m1) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 288:
⊦ ri = ri0 ↔ (∀ key. (key ∈ ri ↔ key ∈ ri0) ∧ (key ∈ ri → ri[key] = ri0[key]))
Proof step 289:
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), ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, m4 ≠ 0 ∨ m1 = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m0 = ROOT_INO, m0 = 0, m1 = 0, m3 = 0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m1) ∈ ro, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, ∀ key. ( key ∈ ((ri0[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str))[inodekey(m0), adr3] ↔ key ∈ (ri0[inodekey(m1), adr1] -- dentrykey(m1, str))[inodekey(m0), adr3] ⊖ ro) ∧ ( key ∈ ((ri0[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str))[inodekey(m0), adr3] → ((ri0[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str))[inodekey(m0), adr3][key] = ((ri0[inodekey(m1), adr1] -- dentrykey(m1, str))[inodekey(m0), adr3] ⊖ 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[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str) )[inodekey(m0), adr3 ], (ri0[inodekey(m1), adr1] -- dentrykey(m1, str) )[inodekey(m0), adr3 ] ⊖ ro] flags: <all paths>

Additional information

Used terms: ((ri0[inodekey(m1), adr1] ⊖ ro) -- dentrykey(m1, str) )[inodekey(m0), adr3 ], (ri0[inodekey(m1), adr1] -- dentrykey(m1, str))[inodekey(m0), adr3] ⊖ ro