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Proof step 12 from proof abs-keys-orphans-add (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
ro.inodes?, ∀ ino. inodekey(ino) ∈ ro ↔ ino = n ∨ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ inodekey(m) ∈ ro ↔ m = n ∨ inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: abs-keys: ⊦ n ∈ abs-keys(ks) ↔ inodekey(n) ∈ ks;% ⊦ inodekey(m).ino = m; (s)% ⊦ inodekey(m).inode?; (s)%⊦ key ∈ orphans(fs, ri) ↔ key.inode? ∧ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ key.ino ≠ ROOT_INO; (s)% ⊦ ino ∈ ns ++ ino0 ↔ ino = ino0 ∨ ino ∈ ns; (s)