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Proof step 138 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(files0, icache, pcache0), m3 ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, ino ∈ files0, m2 ≤ m, ino ∈ icache → ¬ icache[ino].dirty, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ m2 % VFS_PAGE_SIZE = 0, ( ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] → ¬ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty) ∧ ( datakey(ino, n) ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))] → ¬ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))][datakey(ino, n)].dirty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 139:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))][datakey(ino, n)] = mkpentry(boolvar0, buf), afs-cons(dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(files0, icache, pcache0), ino ∈ files0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ pcache0, m3 ∈ files0, m2 ≤ m, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ( ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] → ¬ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty) ∧ ( datakey(ino, n) ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0))] → ¬ boolvar0)

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)) ] [datakey(ino, n) ], boolvar0, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: truncate(m3, m2, pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n0)) ] [datakey(ino, n) ], boolvar0, buf