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Proof step 44 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino ∈ icache ⊦ mkfile(m0, md, m1, content[m, buf]) = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, (files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)])[ino].content), icache[ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
ino ∈ files, ino ∈ icache ⊦ (files[ino].content ⊕ mkcontent(ino, pcache))[m, buf] = files[ino].content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]), icache[ino].inode.directory

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));%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ mkfile(m, md, m0, content).content = content; (s)