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Proof step 2 from proof orphans-cons-reduce (previous step)

orphans-cons(fs, ri, ro) ⊦ orphans-cons(fs0, ri0, ro0) ↔ (∀ ino. (inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro)) → inodekey(ino) ∈ ri0 → (fs0[ri0[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: orphans-cons: ⊦ orphans-cons(fs, ri, ro) ↔ (∀ ino. inodekey(ino) ∈ ri → ( fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro));