[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 190 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[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, m2 ≤ m, asynced1 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ∀ ino. 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].inode.ino = ino ∧ (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty ⊃ valid-file-inode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode, 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)]) ; valid-ino (ino, 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)]) ∧ valid-inode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode, 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)]) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 191:
# 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)]), 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, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino = ino ∧ (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].dirty ⊃ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino ∈ files0 ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.nlink = (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.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[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .nlink ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode = (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].meta, true, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].nlink, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].nsubdirs, dirs[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino].size) ;mkinode (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.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[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .meta, false, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.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[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .nlink, 0, (icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.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[icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino].inode.ino] ) .size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)