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

1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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), ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO, key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro ⊦ key.ino = m8, (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4] ⊖ inodekey(m8))[key] = ((ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5] ⊖ (ro ++ inodekey(m8)))[key], adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, key = inodekey(m0), key = inodekey(m8), key = dentrykey(m0, str0), m = 0, m0 = 0, m0 = m, m5 = 0, m8 = 0, m8 = ROOT_INO, fs0[ri0[inodekey(m8)]].directory, fs0[ri0[inodekey(m5)]].directory, adr1 ∈ log0, adr2 ∈ log0, adr3 ∈ log0, adr4 ∈ log0, adr5 ∈ log0, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], (key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 248:
1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), links(m8, fs0, ri0) = ∅ ++ dentrykey(m0, str0), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), 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[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, key ∈ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0 ⊖ ro, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO ⊦ key.ino = m8, (((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4] ⊖ inodekey(m8))[key] = ((ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5] ⊖ (ro ++ inodekey(m8)))[key], adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, key = dentrykey(m0, str0), key = inodekey(m8), key = inodekey(m0), m = 0, m0 = m, m0 = 0, m5 = 0, m8 = ROOT_INO, m8 = 0, fs0[ri0[inodekey(m5)]].directory, fs0[ri0[inodekey(m8)]].directory, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr5 ∈ log0, adr4 ∈ log0, adr3 ∈ log0, adr2 ∈ log0, adr1 ∈ log0, (key = inodekey(m) ∨ key ≠ dentrykey(m, str) ∧ key ∈ ri0) ∧ ¬ key ∈ ro ∧ ¬ key.data?

Rule argument

fma: key ∈ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2] [inodekey(m), adr3 ] [inodekey(m0), adr4 ]

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s) Used formulas: key ∈ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m0, str0), adr2] [inodekey(m), adr3 ] [inodekey(m0), adr4 ]