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Proof step 3 from proof overwrite-pcache-empty (previous step)

⊦ ∀ ino. (ino ∈ files ⊕ ∅ ↔ ino ∈ files) ∧ (ino ∈ files ⊕ ∅ → (files ⊕ ∅)[ino] = files[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
ino ∈ files ⊦ mkfile(files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, ∅)) = files[ino]

Rule argument

Additional information

Used simplifier rules: in-pcache-overwrite: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files;%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));