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Proof step 280 from proof inv-truncate-buff-none-uncached (previous step)

files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), dcache-cons(dcache, dirs, files0), icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), icache-cons(icache, dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ pcache-cons(truncate(m0, min(m5, m2), pcache0), dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)) ∧ ( asynced2 → synced (files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)))

Heuristic use patterns applied rule cut formula

And obtained the following new goals

Proof step 281:
files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), icache-cons(icache, dirs, files0), icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ pcache-cons(truncate(m0, min(m5, m2), pcache0), dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)) ∧ ( asynced2 → synced (files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0))), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0
Proof step 355:
files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ pcache-cons(truncate(m0, min(m5, m2), pcache0), dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)) ∧ ( asynced2 → synced (files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0))), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

fma: dcache-cons (dcache, dirs, files0 [m0, mkfile (m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ])

Additional information

Used formulas: dcache-cons (dcache, dirs, files0 [m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ])