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Proof step 15 from proof abs-files-del-orphans (previous step)

datakey(ino, n) ∈ ri, inodekey(ino) ∈ ri, fs[ri[inodekey(ino)]].nlink ≠ 0 ∨ ino = ROOT_INO ⊦ fs[ri[inodekey(ino)]].directory, fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO, datakey(ino, n) ∈ ri ⊖ orphans(fs, ri) ∧ fs[(ri ⊖ orphans(fs, ri))[datakey(ino, n)]].data = fs[ri[datakey(ino, n)]].data

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: aubifs-base name: at-dels-ro-data seq: ⊦ datakey(ino, n) ∈ ri ∧ ¬ datakey(ino, n) ∈ ks ∧ ¬ inodekey(ino) ∈ ks → (ri ⊖ ks)[datakey(ino, n)] = ri[datakey(ino, n)] subst: [n, ino, ks, ri] → [n, ino, orphans(fs, ri), ri] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ ¬ datakey(m, m0).inode?; (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s) Used terms: n, ino, orphans(fs, ri), ri