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Proof step 234 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, true, 1, m11, m12), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, true, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), dentrykeys(inodekey(m1), ri0) = ∅, links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), 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), ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (inodekey(m) = key ⊃ adr3;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];(ri0 ⊖ ro)[key])) = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[key], adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, key = inodekey(m1), key = dentrykey(m, str0), key = inodekey(m), m = 0, m1 = ROOT_INO, m1 = 0, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], adr4 ∈ log0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, (key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 235:
fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, true, 1, m11, m12), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, true, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), dentrykeys(inodekey(m1), ri0) = ∅, links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), 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(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(ino) ∈ ri0, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (ri0 ⊖ ro)[datakey(ino, n)] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[datakey(ino, n)], adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), fs0[ri0[inodekey(ino)]].directory, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], adr4 ∈ log0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro

Rule argument

Additional information

Used simplifier rules: 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)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)%⊦ key ∈ ri ⊖ ks ↔ key ∈ ri ∧ ¬ key ∈ ks ∧ (key.data? → ¬ inodekey(key.ino) ∈ ks); (ws)