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Proof step 74 from proof inv-unlink (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, fs0[ri0[dentrykey(ino, str0)]] = dentrynode(key, fs0[ri0[dentrykey(m1, str)]].ino), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, fs0[ri0[inodekey(m1)]].inode?, 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), ri0[dentrykey(ino, str0)] ∈ fs0, dentrykey(m1, str) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, dentrykey(ino, str0) ∈ ri0, inodekey(ino) ∈ ri0, 1 ≤ fs0[ri0[inodekey(m1)]].size, ∀ key. key ∈ links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) ↔ key ∈ ∅ ++ dentrykey(m1, str), fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, dentrykey(ino, str0) = dentrykey(m1, str), ino = 0, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, inodekey(m1) ∈ ro, inodekey(ino) ∈ ro

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, fs0[ri0[dentrykey(ino, str0)]] = dentrynode(key, fs0[ri0[dentrykey(m1, str)]].ino), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(ino)]].directory, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, 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, dentrykey(ino, str0) ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, ri0[dentrykey(ino, str0)] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m1)]].size, ∀ key0. key0 ∈ ri0 ∧ key0.dentry? ∧ fs0[ri0[key0]].ino = fs0[ri0[dentrykey(m1, str)]].ino → key0 = dentrykey(m1, str), fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, dentrykey(ino, str0) = dentrykey(m1, str), ino = 0, m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, inodekey(ino) ∈ ro, inodekey(m1) ∈ ro, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0

Rule argument

Additional information

Used simplifier rules: ⊦ dentrykey(m, str).dentry?; (s)% ⊦ key ∈ ∅ ++ key0 ↔ key = key0; (s)%⊦ key ∈ links(ino, fs, ri) ↔ key ∈ ri ∧ key.dentry? ∧ fs[ri[key]].ino = ino; (s)