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Proof step 3 from proof abs-files-evict (previous step)

⊦ ∀ ino0. (ino0 ∈ abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino ↔ ino0 ∈ abs-files(fs, ri) -- ino) ∧ ( ino0 ∈ abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino → (abs-files(fs, ri \ datakeys(inodekey(ino), ri)) -- ino)[ino0] = (abs-files(fs, ri) -- ino)[ino0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-files: ⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory;%ino ∈ files ⊦ ino ≠ ino0 → (files -- ino0)[ino] = files[ino]; (s)% ⊦ ¬ inodekey(m).data?; (s)%⊦ key ∈ datakeys(key0, ri) ↔ key ∈ ri ∧ key.data? ∧ key0.inode? ∧ key.ino = key0.ino; (s)% ⊦ key ∈ ri \ ks ↔ key ∈ ri ∧ ¬ key ∈ ks; (ws)% ⊦ ¬ key ∈ ri → ri[key] = (∅)[key]; (s)% ⊦ (ri \ datakeys(key, ri))[inodekey(ino)] = ri[inodekey(ino)]; (s)% ⊦ ino ∈ files -- ino0 ↔ ino ≠ ino0 ∧ ino ∈ files; (s)