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Proof step 127 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_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), m2 % VFS_PAGE_SIZE ≠ 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile(m, md, # links(m3, cache_dirs), content0[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))], 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_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = ( 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))] ∧ (asynced0 ↔ asynced1) ∧ some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) = buf-opt0 ∧ mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2) ∧ asynced2 ∧ ESUCCESS = err)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 128:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 129:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = ( 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))] ∧ (asynced0 ↔ asynced1) ∧ some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) = buf-opt0 ∧ mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2) ∧ asynced2 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile(m, md, # links(m3, cache_dirs), content0[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))], m3 ∈ cache_icache ∧ ¬ cache_icache[m3].inode.directory
Proof step 516:
# 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), mkfile(cache_icache[m3].inode.size, cache_icache[m3].inode.meta, cache_icache[m3].inode.nlink, (cache_files ⊕ cache_pcache0)[m3].content) = mkfile(m0, md0, # links(m3, cache_dirs), content0), 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? ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced0 := ?⟩ ( (cache_files ⊕ cache_pcache0) ⊕ cache_icache = ( 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))] ∧ (asynced0 ↔ asynced1) ∧ some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) = buf-opt0 ∧ mkinode(m3, md, false, # links(m3, cache_dirs), 0, m) = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2) ∧ asynced2 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile(m, md, # links(m3, cache_dirs), content0[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))], cache_icache[m3].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [m3, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used terms: m3, cache_icache, cache_files ⊕ cache_pcache0