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Proof step 324 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache)[datakey(m, m3)] = mkpentry(boolvar, buf), buf-opt.some?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(dirs, icache, pcache), datakey(m, m3) ∈ pcache, m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files0) ∧ (¬ pcache[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache[key].page = files0[key.ino].content[key.part]), m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar → m3 ∈ content ∧ buf = content[m3]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 325:
# buf-opt.buf = VFS_PAGE_SIZE, (m = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2));files0[m]) = mkfile(m4, md, m6, content), truncate(m0, min(m5, m2), pcache)[datakey(m, m3)] = mkpentry(boolvar, buf), 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), synced(dirs, icache, pcache), m0 ∈ files0, datakey(m, m3) ∈ pcache, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data?, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ pcache[key].dirty → key.part ∈ files0[key.ino].content ∧ pcache[key].page = files0[key.ino].content[key.part]), m3 * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ m ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # buf = VFS_PAGE_SIZE ∧ m ∈ files0 ∧ (¬ boolvar → m3 ∈ content ∧ buf = content[m3])

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)