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Proof step 247 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, false, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, false, 1, m11, m12), links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.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(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), datakey(ino, n) ∈ ri0, dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, inodekey(ino) ∈ ri0, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1))[datakey(ino, n)] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[datakey(ino, n)], adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, ino = m1, m = 0, m1 = 0, m1 = ROOT_INO, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), fs0[ri0[inodekey(ino)]].directory, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], inodekey(ino) ∈ ro

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 248:
⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)]
Proof step 249:
fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, false, 1, m11, m12), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, false, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), 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), inodekey(ino) ∈ 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, datakey(ino, n) ∈ ri0, datakey(ino, n) ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4], m4 ≠ 0 ∨ m = ROOT_INO ⊦ (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1))[datakey(ino, n)] = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4][datakey(ino, n)], adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, ino = m1, m = 0, m1 = ROOT_INO, m1 = 0, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), fs0[ri0[inodekey(ino)]].directory, inodekey(ino) ∈ ro, 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 ++ inodekey(m1), datakey(ino, n) ∈ ro ++ inodekey(m1)

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [ino, n, ri, ks] → [ino, n, (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2] [inodekey(m), adr3 ] [inodekey(m1), adr4 ], ro ++ inodekey(m1)] flags: <all paths>

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ key ∈ ks ++ key0 ↔ key = key0 ∨ key ∈ ks; (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ ¬ key ∈ ks → (key ∈ ks ++ key0 ↔ key = key0); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s) Used terms: ino, n, (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2] [inodekey(m), adr3 ] [inodekey(m1), adr4 ], ro ++ inodekey(m1)