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Proof step 8 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[adr, fs[ri[key]]][ri[key, adr][inodekey(ino)]].nlink = 0 ∧ ino ≠ ROOT_INO ↔ inodekey(ino) ∈ ro, adr ∈ fs

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 9:
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
Proof step 13:
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, ri[key, adr][inodekey(ino)] = adr, adr ∈ fs

Rule argument

fma: ri[key, adr][inodekey(ino)] = adr

Additional information

Used formulas: ri[key, adr][inodekey(ino)] = adr