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Proof step 144 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), buf-opt.some?, afs-cons(dirs, files0), afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))], m3 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, key.data? ∧ # truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ ( ¬ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key].dirty → key.part ∈ (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) .content ∧ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key].page = (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) .content [key.part ])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 145:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))][key] = mkpentry(boolvar, buf), buf-opt.some?, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache0), m3 ∈ files0, key ∈ truncate(m3, m2, pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0))], m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, key.data? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ ( ¬ boolvar → key.part ∈ (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) .content ∧ buf = (key.ino = m3 ⊃ mkfile(m, md, # links(key.ino, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[key.ino] ) .content [key.part ])

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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ] [key ], boolvar, 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(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)) ] [key ], boolvar, buf