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Proof step 9 from proof abs-keys-orphans (previous step)

ro.inodes?, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ key ∈ ro ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 10:
key.inode?, ro.inodes?, ∀ ino. inodekey(ino) ∈ ro ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ key ∈ ro ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO

Rule argument

fma: key.inode?

Additional information

Used simplifier rules: ⊦ key ∈ ks ∧ ks.inodes? → key.inode?; (ss) Used formulas: key.inode?