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Proof step 316 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), synced(files0, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ino ∈ files0, ino ∈ icache → ¬ icache[ino].dirty, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, ( ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)].dirty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 317:
# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)] = mkpentry(boolvar0, buf), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(files0, icache, pcache0), ino ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ ( ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ boolvar0), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)], boolvar0, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)], boolvar0, buf