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Proof step 138 from proof overwrite-write-page-dirty (previous step)

ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache)[ino0], ino ∈ icache, ino0 ∈ icache ∧ ¬ icache[ino0].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
icache[ino0].inode.directory, ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile(files[ino0].size, files[ino0].meta, files[ino0].nlink, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])), ino ∈ icache

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-no-file: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino];%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));