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Proof step 145 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), 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 ])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 146:
# buf-opt.buf = VFS_PAGE_SIZE, (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] ) = mkfile(m0, md0, m4, content), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, 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), 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? ∧ # buf = VFS_PAGE_SIZE ∧ key.ino ∈ files0 ∧ (¬ boolvar → key.part ∈ content ∧ buf = content[key.part])

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [(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] ), m0, md0, m4, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: (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] ), m0, md0, m4, content