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Proof step 193 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode = mkinode(m0, md0, boolvar, m4, m5, m6), VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), 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), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), m3 ∈ files0, ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, m0 = ino ∧ (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty ⊃ ino ∈ files0 ∧ m4 = (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m4, m5, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .meta, false, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink, 0, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .size) ) )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 194:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar0, inode), inode = mkinode(m0, md0, boolvar, m4, m5, m6), 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)]), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m3 ∈ files0, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, m0 = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m4 = (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink ∧ m5 = 0 ∧ ¬ boolvar ; (ino ∈ dirs ∨ ino ∈ files0) ∧ mkinode(ino, md0, boolvar, m4, m5, m6) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .meta, false, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .nlink, 0, (ino = m3 ⊃ mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ;files0[ino] ) .size) ) )

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [m3, mkientry (false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ] [ino ], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache [m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m)) ] [ino ], boolvar0, inode