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Proof step 5 from proof abs-files-trunc (previous step)

inodekey(ino) ∈ ri ⊦ ¬ fs[ri[inodekey(ino)]].directory ↔ ¬ fs[adr, truncnode(key, n)][ri[inodekey(ino)]].directory, adr ∈ ri

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: ri[inodekey(ino)] = adr

Additional information

Used simplifier rules: ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]; (s)% ⊦ fs[adr, nd][adr] = nd; (s)%key ∈ ri ⊦ ri[key] ∈ ri; (s) Used formulas: ri[inodekey(ino)] = adr