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Proof step 877 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar2, mkinode(m9, md3, boolvar1, m10, m11, m12)), (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), (cache_files ⊕ cache_pcache0)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_files[ino] = mkfile(m8, md1, # 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), m3 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, ino ∈ cache_icache, m3 ∈ cache_icache, m3 ∈ cache_icache ∧ boolvar1, m3 ∈ cache_icache ∧ ¬ boolvar1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0, (n ∈ content ⊕ mkcontent(ino, cache_pcache0) ↔ n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))) ∧ ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) → (content ⊕ mkcontent(ino, cache_pcache0))[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 878:
# buf-opt0.buf = VFS_PAGE_SIZE, (∅)[m3] = mkientry(boolvar2, mkinode(m9, md3, boolvar1, m10, m11, m12)), (∅)[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), 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, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, ino ∈ cache_icache, m3 ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0, (n ∈ content ⊕ mkcontent(ino, cache_pcache0) ↔ n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))) ∧ ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) → (content ⊕ mkcontent(ino, cache_pcache0))[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n])

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)