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Proof step 588 from proof fsync-pages-keep-abs (previous step)

# 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, ⌊err0⌋ ⊦ 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)), icache[ino].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 589:
# buf = VFS_PAGE_SIZE, icache[ino].inode = mkinode(m3, md0, boolvar, m4, m5, m6), files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), ¬ boolvar, files0[ino].content ⊕ mkcontent(ino, pcache) = files1[ino].content ⊕ mkcontent(ino, pcache0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ino ∈ icache, ⌊err0⌋ ⊦ mkfile(m6, md0, m4, files1[ino].content ⊕ mkcontent(ino, pcache0)) = mkfile(m6, md0, m4, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).content ⊕ mkcontent(ino, pcache))

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [icache[ino].inode, m3, md0, boolvar, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache[ino].inode, m3, md0, boolvar, m4, m5, m6