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Proof step 485 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(boolvar0, mkinode(m4, md1, true, m5, m6, m7)), cache_icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m8, m9, m10)), cache_files[ino] = mkfile(m11, md3, # links(ino, cache_dirs), content), 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_files, m3 ∈ cache_files, m3 ∈ cache_icache, ino ∈ 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 = m3, mkfile(m10, md0, m8, content ⊕ mkcontent(ino, cache_pcache0)) = 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))]))

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 486:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 487:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[ino] = mkfile(m11, md3, # links(ino, cache_dirs), content), cache_icache[ino] = mkientry(boolvar, mkinode(m0, md0, false, m8, m9, m10)), cache_icache[m3] = mkientry(boolvar0, mkinode(m4, md1, true, m5, m6, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), 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_icache, m3 ∈ cache_icache, 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, m10 = m10 ∧ md0 = md0 ∧ m8 = m8 ∧ content ⊕ mkcontent(ino, cache_pcache0) = 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))])

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [m, md, m0, content, m1, md0, m2, content0] → [m10, md0, m8, content ⊕ mkcontent(ino, cache_pcache0), 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)) ])] flags: <all paths>

Additional information

Used terms: m10, md0, m8, content ⊕ mkcontent(ino, cache_pcache0), 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)) ])