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Proof step 226 from proof inv-rename-overwrite-keep-parent (previous step)

¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 1, m11, m12), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, 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), key ∈ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ), 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, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO ⊦ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ) [key ] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[key], adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), 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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 227:
⊦ key ∈ ri ∧ ¬ key ∈ ks ∧ ¬ key.data? → (ri ⊖ ks)[key] = ri[key]
Proof step 228:
¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 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), 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, key ∈ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ), boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12 ⊦ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ) [key ] = ((ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ⊖ (ro ++ inodekey(m1)))[key], adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), 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], key ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4] ∧ ¬ key ∈ ro ++ inodekey(m1) ∧ ¬ key.data?
Proof step 258:
¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 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), 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, key ∈ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ), key ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4], boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12 ⊦ (boolvar2 ⊃ ((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] -- inodekey(m1) ;((ri0 ⊖ ro) -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3] ⊖ inodekey(m1) ) [key ] = (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3][inodekey(m1), adr4][key], adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m2 = 0, mkdentry(str, m2) = mkdentry(str0, m1), key.data?, 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], key ∈ ro ++ inodekey(m1)

Rule argument

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

Additional information

Used terms: key, (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2] [inodekey(m), adr3 ] [inodekey(m1), adr4 ], ro ++ inodekey(m1)