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Proof step 15 from proof orphans-cons-gc-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
ri-cons(ri, fs), key ∈ ri, inodekey(ino) ∈ ri, ∀ ino. inodekey(ino) ∈ ri → (fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro) ⊦ fs[ri[inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, ri[inodekey(ino)] = adr, inodekey(ino) = key, adr ∈ fs

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)