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Proof step 138 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, key = dentrykey(m, str0) ∨ key ∈ ri0 ⊖ ro ⊦ (dentrykey(m, str0) = key ⊃ adr2;(ri0 ⊖ ro)[key]) = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro)[key], adr1 = adr2, adr1 = adr3, adr2 = adr3, key = inodekey(m), key = dentrykey(m, str), 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 = dentrykey(m, str0) ∨ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 139:
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, key = dentrykey(m, str0) ∨ key ∈ ri0 ⊖ ro, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (dentrykey(m, str0) = key ⊃ adr2;(ri0 ⊖ ro)[key]) = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ ro)[key], adr1 = adr3, adr1 = adr2, adr2 = adr3, key = dentrykey(m, str), key = inodekey(m), key = dentrykey(m, str0), 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 = dentrykey(m, str0) ∨ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Rule argument

fma: key = dentrykey(m, str0)

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ ks.inodes? → ¬ dentrykey(ino, str) ∈ ks; (s)% ⊦ ¬ dentrykey(m, str).data?; (s) Used formulas: key = dentrykey(m, str0)