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Proof step 243 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, (ino = 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) ;cache_files[ino] ) = mkfile(m11, md3, m12, content), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, (∅)[m3] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))][ino] = mkientry(boolvar1, mkinode(m0, md0, false, m8, m9, m10)), 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), ino ∈ cache_files, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))], m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, (ino = 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)[ino] ) = mkfile (m10, md0, m8, content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), m3 ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 244:
⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]
Proof step 245:
# buf-opt0.buf = VFS_PAGE_SIZE, (ino = 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) ;cache_files[ino] ) = mkfile(m11, md3, m12, content), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))][ino] = mkientry(boolvar1, mkinode(m0, md0, false, m8, m9, m10)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[m3] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), ino = m3, 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), ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))], m3 ∈ cache_files, ino ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, (ino = 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)[ino] ) = mkfile (m10, md0, m8, content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), m3 ∈ cache_icache
Proof step 298:
# buf-opt0.buf = VFS_PAGE_SIZE, (ino = 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) ;cache_files[ino] ) = mkfile(m11, md3, m12, content), VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[ino] = mkientry(boolvar1, mkinode(m0, md0, false, m8, m9, m10)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[m3] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), 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), ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))], m3 ∈ cache_files, ino ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, (ino = 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)[ino] ) = mkfile (m10, md0, m8, content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), ino = m3, m3 ∈ cache_icache

Rule argument

spec: store, inst: icache name: At-other seq: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino] subst: [ino, ino0, icache, ie] → [ino, m3, cache_icache, mkientry (false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] flags: <all paths>

Additional information

Used terms: ino, m3, cache_icache, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))