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Proof step 1184 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_icache[m] = mkientry(boolvar0, mkinode(m0, md0, false, # links(m, cache_dirs), m11, m12)), 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), m ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ∀ n. ( n ∈ (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2) ↔ n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))) ∧ ( n ∈ (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2) → ((content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2))[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n]), m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1185:
# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar0, mkinode(m0, md0, false, # links(m, cache_dirs), m11, m12)), cache_files[m] = mkfile(m1, md2, # links(m, 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), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0, ( n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) ↔ n ∈ (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))) ∧ ( n * VFS_PAGE_SIZE < min(m8, m2) ∧ n ∈ content1 ⊕ mkcontent(m, cache_pcache0) → (content1 ⊕ mkcontent(m, cache_pcache0))[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n])

Rule argument

Additional information

Used simplifier rules: ⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ∈ content upto n ↔ m * VFS_PAGE_SIZE < n ∧ m ∈ content; (s)