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Proof step 332 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, (files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache[datakey(m, n), mkpentry(false, buf)])[ino].content), icache[ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 333:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), files0[ino].content ⊕ mkcontent(ino, pcache) = files1[ino].content ⊕ mkcontent(ino, pcache0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files1[ino].content ⊕ mkcontent(ino, pcache0)) = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).content ⊕ mkcontent(ino, pcache[datakey(m, n), mkpentry(false, buf)])), icache[ino].inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ 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)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ 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); (s)