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Proof step 169 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m6)] = mkpentry(false, content0[m6]), buf-opt.some?, m6 * VFS_PAGE_SIZE < m2, m6 * VFS_PAGE_SIZE < m, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(dirs, icache, pcache0), m6 ∈ content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)], m6 ∈ content0, datakey(m3, m6) ∈ pcache0, m3 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files0 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files0[key0.ino].content ∧ pcache0[key0].page = files0[key0.ino].content[key0.part]), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, content0[m6] = content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)][m6], datakey(m3, m6) = datakey(m3, m2 / VFS_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: file-content name: At-other seq: ⊦ n ≠ n0 → content[n0, buf][n] = content[n] subst: [n, buf, n0, content] → [m6, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0] flags: <all paths>

Additional information

Used terms: m6, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0