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Proof step 187 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m7)] = mkpentry(false, content0[m7]), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), m7 * VFS_PAGE_SIZE < m2, m7 * VFS_PAGE_SIZE < m, afs-cons (dirs, files1 [m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ]), afs-cons(dirs, files1), synced(dirs, icache, pcache0), m7 ∈ content0, m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, datakey(m3, m7) ∈ pcache0, m7 ∈ content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)], m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, ∀ key0. key0 ∈ pcache0 → key0.data? ∧ # pcache0[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache0[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache0[key0].page = files1[key0.ino].content[key0.part]) ⊦ m2 % VFS_PAGE_SIZE = 0, content0[m7] = content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)][m7], datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0

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] → [m7, fill (content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used terms: m7, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0), m2 / VFS_PAGE_SIZE, content0