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Proof step 14 from proof orphans-cons-gc-one (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 15:
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

Rule argument

fma: inodekey(ino) = key

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s) Used formulas: inodekey(ino) = key