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Proof step 11 from proof overwrite-pcache-empty (previous step)

files[ino] = mkfile(m, md, m0, content), ino ∈ files ⊦ ∀ n. (n ∈ content ⊕ mkcontent(ino, ∅) ↔ n ∈ content) ∧ (content ⊕ mkcontent(ino, ∅))[n] = content[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
files[ino] = mkfile(m, md, m0, content), ino ∈ files ⊦ (n ∈ content → n ∈ content ⊕ mkcontent(ino, ∅)) ∧ (content ⊕ mkcontent(ino, ∅))[n] = content[n]

Rule argument

Additional information

Used simplifier rules: in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ ¬ key ∈ ∅; (s)