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Proof step 246 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[m0] = mkfile(m1, md2, # links(m0, cache_dirs), content1), (∅)[m0] = 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), m0 ∈ cache_files, m2 ≤ m10, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, mkfile (m10, md0, # links(m0, cache_dirs), (content1 ⊕ mkcontent(m0, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) = mkfile (m10, md0, # links(m0, cache_dirs), (content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ⊕ mkcontent (m0, truncate(m0, m2, cache_pcache0)[datakey(m0, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])), m0 ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 247:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 248:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, (∅)[m0] = mkientry(boolvar0, mkinode(m4, md1, boolvar, m5, m6, m7)), cache_files[m0] = mkfile(m1, md2, # links(m0, 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), m0 ∈ cache_files, m2 ≤ m10, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, m0 ∈ cache_icache, m10 = m10 ∧ md0 = md0 ∧ # links(m0, cache_dirs) = # links(m0, cache_dirs) ∧ (content1 ⊕ mkcontent(m0, cache_pcache0))[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2 = (content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ⊕ mkcontent (m0, truncate(m0, m2, cache_pcache0)[datakey(m0, 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, # links(m0, cache_dirs), (content1 ⊕ mkcontent(m0, cache_pcache0) )[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2, m10, md0, # links(m0, cache_dirs), ( content1 [m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ⊕ mkcontent (m0, truncate(m0, m2, cache_pcache0) [datakey(m0, 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, # links(m0, cache_dirs), (content1 ⊕ mkcontent(m0, cache_pcache0) )[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2, m10, md0, # links(m0, cache_dirs), ( content1 [m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1) ] upto m2) ⊕ mkcontent (m0, truncate(m0, m2, cache_pcache0) [datakey(m0, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ])