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Proof step 5 from proof pcache-overwrite-read-page (previous step)

files[ino] = mkfile(m, md, m0, content), ino ∈ files, n ∈ content ⊦ datakey(ino, n) ∈ pcache, ∀ ino0. (ino0 ∈ files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])] ↔ ino0 ∈ files ⊕ pcache) ∧ ( ino0 ∈ files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])] → (files ⊕ pcache[datakey(ino, n), mkpentry(false, content[n])])[ino0] = (files ⊕ pcache)[ino0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ mkfile (files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])])) = mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)), datakey(ino, n) ∈ pcache

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));