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Proof step 206 from proof inv-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m3 % VFS_PAGE_SIZE, fs0[ri0[inodekey(m)]] = inodenode(key, md, false, m0, m1, m2), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, ro.inodes?, fo.inodes?, buf-opt.some?, 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), adr2 ∈ (ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m3 ≤ n1 ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(m) ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO

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 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro] flags: <all paths>

Additional information

Used terms: adr2, (ri0 \ datakeys(inodekey(m), m3, ri0)) ⊖ ro