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Proof step 250 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, 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) ⊦ ⟪pcache_truncate#(m0, m2, m5; err, pcache); inode0 := mkinode(m0, md0, false, # links(m0, dirs), 0, m5); ino := m0; files := files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))]; skip; skip⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], pcache) ∧ ( asynced1 → synced (files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], pcache))), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 251:
# 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[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) ⊦ ⟪if ∀ key. key ∈ pcache → key.data? then pcache := truncate(ino, min(n, size), pcache) else abort; inode0 := mkinode(m0, md0, false, # links(m0, dirs), 0, m5); ino := m0; files := files0[m0, mkfile(m1, md1, # links(m0, dirs), content0 upto min(m5, m2))]; skip; skip⟫ ( icache-cons (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ dcache-cons(dcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ pcache-cons(pcache, dirs, files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta]) ∧ synced(dirs, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], pcache) ∧ ( asynced1 → synced (files[ino, (ino ∈ files ⊃ files[ino].size:= inode0.size;files[ino]).meta:= inode0.meta], icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], pcache))), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_truncate#(INO, SIZE, N; ERR, PCACHE) {if ∀ key. key ∈ PCACHE → key.data? then PCACHE := truncate(INO, min(N, SIZE), PCACHE) else abort };