[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 522 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_icache, m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))]

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 523:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 524:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, m3 ∈ cache_icache, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ∀ ino. ( ino ∈ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ↔ ino ∈ ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))]) ∧ ( ino ∈ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] → ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] [ino ] = ( ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] )[ino ])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files, files0] → [((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0) )[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ], ( cache_files [m3, mkfile (m, md, # links(m3, cache_dirs), content1 [m2 / VFS_PAGE_SIZE, fill (buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ]) ⊕ cache_icache [m3, mkientry (false, mkinode (m3, md, false, # links(m3, cache_dirs), 0, m)) ]] flags: <all paths>

Additional information

Used terms: ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m, md, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0) )[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ], ( cache_files [m3, mkfile (m, md, # links(m3, cache_dirs), content1 [m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ]) ⊕ cache_icache [m3, mkientry (false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m)) ]