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Proof step 12 from proof abs-orphans-diff-datakeys (previous step)

links(ino0, abs-dirs(fs, ri)) = ∅, fs[(ri \ datakeys(inodekey(ino), n, ri))[inodekey(ino0)]].directory, inodekey(ino0) ∈ ri ⊦ ino0 = ROOT_INO, fs[ri[inodekey(ino0)]].directory

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: inodekey(ino0) ∈ datakeys(inodekey(ino), n, ri)

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ks → (ri \ ks)[key] = ri[key]; (s)%⊦ key ∈ datakeys(key0, n, ri) ↔ key ∈ datakeys(key0, ri) ∧ n ≤ key.part * VFS_PAGE_SIZE; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ ¬ inodekey(m).data?; (s) Used formulas: inodekey(ino0) ∈ datakeys(inodekey(ino), n, ri)