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Proof step 12 from proof abs-keys-orphans-add2 (previous step)

key = inodekey(m), key.inode?, ∀ ino. inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ ino = n ∨ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ key ∈ ri0 ∧ fs0[ri0[key]].nlink = 0 ∧ m ≠ ROOT_INO ↔ key = inodekey(n) ∨ key ∈ ri ∧ fs[ri[key]].nlink = 0 ∧ m ≠ ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ ino. inodekey(ino) ∈ ri0 ∧ fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ ino = n ∨ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ⊦ inodekey(m) ∈ ri0 ∧ fs0[ri0[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO ↔ m = n ∨ inodekey(m) ∈ ri ∧ fs[ri[inodekey(m)]].nlink = 0 ∧ m ≠ ROOT_INO

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)