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Proof step 151 from proof inv-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, inode), datakey(ino, n).data?, afs-cons(dirs, files1), 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) ]), synced(dirs, icache, pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ files1, ino ∈ dirs, datakey(ino, n) ∈ pcache0, m2 ≤ m, ino ∈ icache → ¬ boolvar0, asynced2 → synced(files1, icache, pcache0), ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data?, datakey(ino, n).part * VFS_PAGE_SIZE < m2 ∨ m3 ≠ datakey(ino, n).ino ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 152:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar0, inode), pcache0[datakey(ino, n)] = mkpentry(true, buf), files1[m3] = mkfile(m1, md1, # links(m3, dirs), content0), 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), datakey(ino, n) ∈ pcache0, ino ∈ dirs, m3 ∈ files1, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, asynced2 → synced(files1, icache, pcache0), ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).data?; (s)