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Proof step 927 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), cache_icache[m3] = mkientry(boolvar1, mkinode(m0, md0, false, # links(m3, cache_dirs), m10, m11)), 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_icache, m3 ∈ cache_files, ino ∈ cache_files, n ∈ content ⊕ mkcontent(ino, cache_pcache0), n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)), n ∈ mkcontent(ino, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ mkcontent(ino, cache_pcache0)[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n], ino ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 928:
# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar1, mkinode(m0, md0, false, # links(m3, cache_dirs), m10, m11)), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), 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), n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)), n ∈ content ⊕ mkcontent(ino, cache_pcache0), ino ∈ cache_files, m3 ∈ cache_files, m3 ∈ cache_icache, datakey(ino, n) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ cache_pcache0[datakey(ino, n)].page = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n], ino ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)