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Proof step 258 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), err = ESUCCESS, ino = m0, n = m5, size = m2, buf-opt.some?, 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, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] [m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] ⊃ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] .size:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).size ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] ) .meta:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).meta ]) ∧ dcache-cons (dcache, dirs, files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] [m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] ⊃ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] .size:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).size ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] ) .meta:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).meta ]) ∧ pcache-cons (truncate(ino, min(n, size), pcache), dirs, files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] [m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] ⊃ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] .size:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).size ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] ) .meta:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).meta ]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(ino, min(n, size), pcache)) ∧ ( asynced1 → synced (files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] [m0, (m0 ∈ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))] ⊃ files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] .size:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).size ;files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))][m0] ) .meta:= mkinode(m0, md0, false, # links(m0, dirs), 0, m5).meta ], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(ino, min(n, size), pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 259:
# 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), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files0), synced(dirs, icache, pcache), m0 ∈ files0, asynced1 → synced(files0, icache, pcache), ∀ key. key ∈ pcache → key.data? ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, 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))]) ∧ dcache-cons(dcache, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ pcache-cons(truncate(m0, min(m5, m2), pcache), 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), pcache)) ∧ ( asynced1 → 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), pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)