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Proof step 7 from proof datakeys-set-add (previous step)

key0 ∈ ri ∧ key0.data? ∧ inodekey(key0.ino) ∈ ks ∨ key0 ∈ ri ∧ key0.data? ∧ key.inode? ∧ key0.ino = key.ino ⊦ key0 ∈ ri ∧ key0.data? ∧ (inodekey(key0.ino) = key ∨ inodekey(key0.ino) ∈ ks)

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ key.inode? → inodekey(key.ino) = key; (s)