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Proof step 119 from proof inv-rename-new-keep-parent (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, dentrykey(m, str) ∈ ri0, 1 ≤ m6, boolvar2 → 1 ≤ m5, m4 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m0 = 0, m6 = 0, adr2 ∈ ri0 -- dentrykey(m, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, ∀ key. ( key ∈ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ↔ key ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro) ∧ ( key ∈ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] → ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][key] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro)[key])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 120:
fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), 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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m6, boolvar2 → 1 ≤ m5, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size, m4 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m0 = 0, m6 = 0, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), ( key = inodekey(m) ∨ key = dentrykey(m, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro ↔ key ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro) ∧ ( key = inodekey(m) ∨ key = dentrykey(m, str0) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro → (inodekey(m) = key ⊃ adr3;(dentrykey(m, str0) = key ⊃ adr2;(dentrykey(m, str) = key ⊃ (∅)[dentrykey(m, str)];(ri0 ⊖ ro)[key]))) = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro)[key])

Rule argument

Additional information

Used simplifier rules: in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)