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Proof step 225 from proof inv-rename-overwrite-reparent (previous step)

1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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), key ∈ ri0, ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, key.data? → key.ino ≠ m8 ∧ ¬ inodekey(key.ino) ∈ ro, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, key = inodekey(m8), key = dentrykey(m, str), m = 0, m0 = 0, m0 = m, m5 = 0, m8 = 0, m8 = ROOT_INO, fs0[ri0[inodekey(m8)]].directory, fs0[ri0[inodekey(m5)]].directory, key ∈ ro, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr5 ∈ log0, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], (key = inodekey(m0) ∨ key = inodekey(m) ∨ key = dentrykey(m0, str0) ∨ (key.data? → ¬ inodekey(key.ino) ∈ ro)) ∧ (key.data? → key.ino ≠ m8)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: key.data?

Additional information

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