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Proof step 6 from proof abs-files-evict (previous step)

⊦ (ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[(∅)[inodekey(ino0)]].directory → inodekey(ino0) ∈ ri) ∧ ( ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[ri[inodekey(ino0)]].directory → abs-files(fs, ri \ datakeys(inodekey(ino), ri))[ino0] = abs-files(fs, ri)[ino0])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
inodekey(ino0) ∈ ri ⊦ (ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[(∅)[inodekey(ino0)]].directory → inodekey(ino0) ∈ ri) ∧ ( ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[ri[inodekey(ino0)]].directory → abs-files(fs, ri \ datakeys(inodekey(ino), ri))[ino0] = abs-files(fs, ri)[ino0])
Proof step 10:
⊦ inodekey(ino0) ∈ ri, (ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[(∅)[inodekey(ino0)]].directory → inodekey(ino0) ∈ ri) ∧ ( ino0 ≠ ino ∧ inodekey(ino0) ∈ ri \ datakeys(inodekey(ino), ri) ∧ ¬ fs[ri[inodekey(ino0)]].directory → abs-files(fs, ri \ datakeys(inodekey(ino), ri))[ino0] = abs-files(fs, ri)[ino0])

Rule argument

fma: inodekey(ino0) ∈ ri

Additional information

Used formulas: inodekey(ino0) ∈ ri