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Proof step 392 from proof inv-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), m0 ∈ files0, datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ ∀ ino. ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = ino ∧ (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty ⊃ valid-file-inode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ; valid-ino(ino, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ∧ valid-inode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode, dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]) ), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 393:
# buf0 = VFS_PAGE_SIZE, pcache0[datakey(m0, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), icache-cons(icache, dirs, files0), synced(dirs, icache, pcache0), ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m0 ∈ files0, asynced2 → synced(files0, icache, pcache0), ∀ key. key ∈ pcache0 → key.data? ⊦ m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = ino ∧ (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty ⊃ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino ∈ files0 ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.nlink = (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .nlink ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.nsubdirs = 0 ∧ ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode = (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino ∈ dirs ⊃ mkinode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].meta, true, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].nlink, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].nsubdirs, dirs[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino].size) ;mkinode (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .meta, false, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino] ) .nlink, 0, (icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].inode.ino = m0 ⊃ mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2)) ;files0[icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][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)