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Proof step 129 from proof inv-rename-overwrite-keep-parent (previous step)

fs0[ri0[inodekey(m1)]] = inodenode(key1, md0, boolvar0, 1, m9, m10), fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(ino, str)]] = dentrynode(key0, m1), links(m1, fs0, ri0) = ∅ ++ dentrykey(ino, str1), fs0[ri0[inodekey(ino)]].directory, 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), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(ino, str) ∈ ri0, ri0[dentrykey(ino, str)] ∈ fs0, ri0[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(ino)] ∈ fs0, dentrykey(ino, str1) ∈ ri0, inodekey(m1) ∈ ri0, inodekey(ino) ∈ ri0, boolvar0 → dentrykeys(inodekey(m1), ri0) = ∅, m4 ≠ 0 ∨ ino = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10 ⊦ adr1 = adr2, adr1 = adr4, adr1 = adr3, adr2 = adr4, adr2 = adr3, adr3 = adr4, ino = 0, m1 = 0, m1 = ROOT_INO, str = str1, adr3 ∈ (ri0 -- dentrykey(ino, str))[dentrykey(ino, str1), adr2], adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(ino, str), adr4 ∈ (ri0 -- dentrykey(ino, str))[dentrykey(ino, str1), adr2][inodekey(ino), adr3], inodekey(m1) ∈ ro, inodekey(ino) ∈ ro

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 131:
fs0[ri0[dentrykey(ino, str)]] = dentrynode(key0, m1), fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key1, md0, boolvar0, 1, m9, m10), fs0[ri0[inodekey(ino)]].directory, 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), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), inodekey(ino) ∈ ri0, inodekey(m1) ∈ ri0, dentrykey(ino, str1) ∈ ri0, ri0[inodekey(ino)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(ino, str1)] ∈ fs0, ri0[dentrykey(ino, str)] ∈ fs0, dentrykey(ino, str) ∈ ri0, boolvar0 → dentrykeys(inodekey(m1), ri0) = ∅, ∀ key. key ∈ links(m1, fs0, ri0) ↔ key ∈ ∅ ++ dentrykey(ino, str1), ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar0 ∧ boolvar2 ∧ m6 = m10, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ ino = ROOT_INO ⊦ adr1 = adr3, adr1 = adr4, adr1 = adr2, adr2 = adr3, adr2 = adr4, adr3 = adr4, ino = 0, m1 = ROOT_INO, m1 = 0, str = str1, inodekey(ino) ∈ ro, inodekey(m1) ∈ ro, adr4 ∈ (ri0 -- dentrykey(ino, str))[dentrykey(ino, str1), adr2][inodekey(ino), adr3], adr2 ∈ ri0 -- dentrykey(ino, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, adr3 ∈ (ri0 -- dentrykey(ino, str))[dentrykey(ino, str1), adr2]

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [∅ ++ dentrykey(ino, str1), links(m1, fs0, ri0)] flags: <all paths>

Additional information

Used terms: ∅ ++ dentrykey(ino, str1), links(m1, fs0, ri0)