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Proof step 9 from proof orphans-cons-gc-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
ri[key, adr][inodekey(ino)] = adr, ri-cons(ri, fs), key ∈ ri, inodekey(ino) ∈ ri[key, adr], ∀ ino. inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro) ⊦ fs[ri[key]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr ∈ fs

Rule argument

Additional information

Used simplifier rules: ⊦ adr = adr0 → fs[adr0, nd][adr] = nd; (s)