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Proof step 123 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?, 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, key0.data? → ¬ inodekey(key0.ino) ∈ ro, m0 ≠ 0 ∨ m = ROOT_INO, key0 = inodekey(m) ∨ key0 ∈ ri0 ∧ (¬ key0.data? ∨ key0.ino ≠ m ∨ ¬ m3 ≤ key0.part * VFS_PAGE_SIZE) ⊦ 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, inodekey(m) ∈ ro, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, key0 ∈ ro, m0 = 0 ∧ m ≠ ROOT_INO, (key0 = datakey(m, m3 / VFS_PAGE_SIZE) ∨ key0 ∈ ri0) ∧ (key0 ≠ datakey(key0.ino, m3 / VFS_PAGE_SIZE) ∧ ¬ key0 ∈ ri0 ∨ ¬ key0.data? ∨ key0.ino ≠ m ∨ ¬ m3 ≤ key0.part * VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: key0.data?

Additional information

Used simplifier rules: elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0).part = m0; (s) Used formulas: key0.data?