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Proof step 140 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, fo.inodes?, ro.inodes?, buf-opt.some?, m3 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < n1, m3 / VFS_PAGE_SIZE * VFS_PAGE_SIZE < m3, 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), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, m3 ≤ n1, m0 ≠ 0 ∨ m = ROOT_INO ⊦ m3 % VFS_PAGE_SIZE = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, inodekey(m) ∈ (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2] ⊖ ro, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, inodekey(m) ∈ ro, datakey(m, m3 / VFS_PAGE_SIZE) ∈ ri0, m0 = 0 ∧ m ≠ ROOT_INO

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: in-dels-ro seq: ⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks) subst: [key, ri, ks] → [inodekey(m), (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2], ro] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ ¬ inodekey(m).data?; (s) Used terms: inodekey(m), (ri0 \ datakeys(inodekey(m), m3, ri0))[inodekey(m), adr2], ro