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Proof step 319 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), key = datakey(m, m3), key.data?, buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), key ∈ pcache, m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ # truncate(m0, min(m5, m2), pcache)[key].page = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache)[key].dirty → m3 ∈ (m = m0 ⊃ mkfile(m5, md0, # links(m, dirs), content0 upto min(m5, m2));files0[m]).content ∧ truncate(m0, min(m5, m2), pcache)[key].page = (m = m0 ⊃ mkfile(m5, md0, # links(m, dirs), content0 upto min(m5, m2));files0[m]).content[m3]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 320:
# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), buf-opt.some?, afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, datakey(m, m3) ∈ pcache, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data?, m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # truncate(m0, min(m5, m2), pcache)[datakey(m, m3)].page = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache)[datakey(m, m3)].dirty → m3 ∈ (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).content ∧ truncate(m0, min(m5, m2), pcache)[datakey(m, m3)].page = (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]).content[m3])

Rule argument

Additional information

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