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Proof step 431 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0], ino ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 432:
⊦ 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)
Proof step 433:
files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0], ino ∈ icache, ino0 ∈ icache ∧ ¬ icache[ino0].inode.directory
Proof step 579:
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

Rule argument

spec: <toplevel> name: at-icache-overwrite seq: ⊦ 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) subst: [ino, icache, files] → [ino0, icache, files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]] flags: <all paths>

Additional information

Used terms: ino0, icache, files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]