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Proof step 114 from proof inv-unlink (previous step)

fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, false, 1, m6, m7), fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m0), fs0[ri0[inodekey(m1)]] = inodenode(key0, md1, true, m3, m4, m + 1), links(m0, fs0, ri0) = ∅ ++ dentrykey(m1, str), 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), key2 ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, key2.data? → ¬ inodekey(key2.ino) ∈ ro, m3 ≠ 0 ∨ m1 = ROOT_INO ⊦ (ri0[inodekey(m1), adr1] ⊖ ro)[key2] = adr3, adr1 = adr3, adr1 = (ri0[inodekey(m1), adr1] ⊖ ro)[key2], m0 = 0, m0 = ROOT_INO, m1 = 0, key2 ∈ ro, inodekey(m1) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, (ri0[inodekey(m1), adr1] ⊖ ro)[key2] ∈ fs0, adr3 ∈ fs0, adr3 ∈ log0, (ri0[inodekey(m1), adr1] ⊖ ro)[key2] ∈ log0, adr1 ∈ log0, key2 ∈ ri0[inodekey(m1), adr1] ∧ ¬ key2 ∈ ro ∧ ¬ key2.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
fs0[ri0[inodekey(m0)]] = inodenode(key1, md2, false, 1, m6, m7), fs0[ri0[dentrykey(m1, str)]] = dentrynode(key, m0), fs0[ri0[inodekey(m1)]] = inodenode(key0, md1, true, m3, m4, m + 1), links(m0, fs0, ri0) = ∅ ++ dentrykey(m1, str), 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), datakey(ino, n) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, inodekey(m0) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, inodekey(ino) ∈ ri0, m3 ≠ 0 ∨ m1 = ROOT_INO ⊦ (ri0[inodekey(m1), adr1] ⊖ ro)[datakey(ino, n)] = adr3, adr1 = adr3, adr1 = (ri0[inodekey(m1), adr1] ⊖ ro)[datakey(ino, n)], m0 = 0, m0 = ROOT_INO, m1 = 0, fs0[ri0[inodekey(ino)]].directory, inodekey(m1) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, (ri0[inodekey(m1), adr1] ⊖ ro)[datakey(ino, n)] ∈ fs0, adr3 ∈ fs0, adr3 ∈ log0, (ri0[inodekey(m1), adr1] ⊖ ro)[datakey(ino, n)] ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%elim-data: ⊦ key.data? ↔ (∃ ino, n. key = datakey(ino, n));%ubifs-file-in: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → inodekey(ino) ∈ ri; (forward) from specification aubifs-inv%ubifs-file-notdir: ⊦ datakey(ino, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ fs[ri[inodekey(ino)]].directory; (forward) from specification aubifs-inv% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)