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Proof step 148 from proof inv-rmdir (previous step)

fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m3, m + 1, m1 + 1), fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md2, true, 1, m5, m6), dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m0, 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), inodekey(ino) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(m2) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, ri0[inodekey(m0)] ∈ fs0, datakey(ino, n) ∈ ri0, datakey(ino, n) ∈ (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3], m3 ≠ 0 ∨ m0 = ROOT_INO ⊦ (ri0[inodekey(m0), adr1] ⊖ ro)[datakey(ino, n)] = (ri0[inodekey(m0), adr1] -- dentrykey(m0, str))[inodekey(m2), adr3][datakey(ino, n)], adr1 = adr3, adr1 = adr2, adr2 = adr3, m0 = 0, m2 = 0, m2 = ROOT_INO, fs0[ri0[inodekey(ino)]].directory, inodekey(ino) ∈ ro, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, inodekey(m2) ∈ ro, inodekey(m0) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, inodekey(ino) ∈ ro ++ inodekey(m2), datakey(ino, n) ∈ ro ++ inodekey(m2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 149:
fs0[ri0[inodekey(m2)]] = inodenode(key1, md2, true, 1, m5, m6), fs0[ri0[dentrykey(m0, str)]] = dentrynode(key, m2), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m3, m + 1, m1 + 1), dentrykeys(inodekey(m2), ri0) = ∅, links(m2, fs0, ri0) = ∅ ++ dentrykey(m0, str), 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, ri0[inodekey(m0)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m0, str)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m0, str) ∈ ri0, inodekey(ino) ∈ ri0, m3 ≠ 0 ∨ m0 = ROOT_INO ⊦ (ri0[inodekey(m0), adr1] ⊖ ro)[datakey(ino, n)] = ri0[datakey(ino, n)], adr1 = adr2, adr1 = adr3, adr2 = adr3, ino = m2, m0 = 0, m2 = ROOT_INO, m2 = 0, fs0[ri0[inodekey(ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m0) ∈ ro, inodekey(m2) ∈ ro, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, inodekey(ino) ∈ ro

Rule argument

Additional information

Used simplifier rules: at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ ¬ key ∈ ks → (key ∈ ks ++ key0 ↔ key = key0); (s)% ⊦ ks.inodes? → ¬ datakey(ino, n) ∈ ks; (s)% ⊦ key ∈ ks ++ key0 ↔ ¬(key ≠ key0 ∧ ¬ key ∈ ks); (ss)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ datakey(m, m0) ≠ dentrykey(m1, str); (s)% ⊦ inodekey(m) ≠ datakey(m0, m1); (s)