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Proof step 14 from proof abs-dirs-unused-adrs (previous step)

range ri ∩ as = ∅, fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri, dentrykey(ino, str) ∈ ri ⊦ (fs \ as)[ri[dentrykey(ino, str)]].ino = fs[ri[dentrykey(ino, str)]].ino

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: ri[dentrykey(ino, str)] ∈ as

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ as → (fs \ as)[adr] = fs[adr]; (s)% ⊦ adr ∈ as → (fs \ as)[adr] = (∅)[adr]; (s)%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store]% ⊦ key ∈ ri ∧ as ∩ range ri = ∅ → ¬ ri[key] ∈ as; (s) Used formulas: ri[dentrykey(ino, str)] ∈ as