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Proof step 579 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = mkfile (icache[ino0].inode.size, icache[ino0].inode.meta, icache[ino0].inode.nlink, (files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)])[ino0].content), icache[ino0].inode.directory, ino ∈ icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 580:
files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ mkfile(icache[ino0].inode.size, icache[ino0].inode.meta, icache[ino0].inode.nlink, files[ino0].content ⊕ mkcontent(ino0, pcache)) = mkfile (icache[ino0].inode.size, icache[ino0].inode.meta, icache[ino0].inode.nlink, files[ino0].content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])), icache[ino0].inode.directory, ino ∈ icache

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content);%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)