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Proof step 8 from proof abs-keys-orphans-add (previous step)

abs-keys(ro) = abs-keys(orphans(fs, ri)) ++ n, key.inode?, ro.inodes? ⊦ key ∈ ro ↔ key = inodekey(n) ∨ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
abs-keys(ro) = abs-keys(orphans(fs, ri)) ++ n, key = inodekey(m), key.inode?, ro.inodes? ⊦ key ∈ ro ↔ key = inodekey(n) ∨ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

spec: key name: elim-01 seq: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)) subst: [key, m] → [key, m]

Additional information

Used simplifier rules: ⊦ key.inode? → (m = key.ino ↔ key = inodekey(m)); (elim) Used terms: key, m