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Proof step 357 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ∀ key. key ∈ truncate(m0, min(m5, m2), pcache0) → key.data? ∧ # truncate(m0, min(m5, m2), pcache0)[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[key].dirty → key.part ∈ files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))][key.ino].content ∧ truncate(m0, min(m5, m2), pcache0)[key].page = files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))][key.ino].content[key.part]), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 358:
# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), key.data?, afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, key ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data?, key.part * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ key.ino ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, # truncate(m0, min(m5, m2), pcache0)[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ ( ¬ truncate(m0, min(m5, m2), pcache0)[key].dirty → key.part ∈ (key.ino = m0 ⊃ mkfile(m5, md0, # links(key.ino, dirs), content0 upto min(m5, m2));files0[key.ino]).content ∧ truncate(m0, min(m5, m2), pcache0)[key].page = (key.ino = m0 ⊃ mkfile(m5, md0, # links(key.ino, dirs), content0 upto min(m5, m2));files0[key.ino]).content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ key ∈ truncate(ino, size, pcache) ↔ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino); (s)