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Proof step 6 from proof abs-keys-orphans2 (previous step)

abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)), key.inode? ⊦ key.ino = ROOT_INO, key ∈ ri0 ∧ fs0[ri0[key]].nlink = 0 ↔ key ∈ ri ∧ fs[ri[key]].nlink = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
abs-keys(orphans(fs0, ri0)) = abs-keys(orphans(fs, ri)), key = inodekey(m), key.inode? ⊦ key ∈ ri0 ∧ fs0[ri0[key]].nlink = 0 ↔ 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