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Proof step 1121 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), 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? ⊦ (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2) = (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1122:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 1123:
# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_icache[m] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), 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

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content, content0] → [(content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2), (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))] flags: <all paths>

Additional information

Used terms: (content1 ⊕ mkcontent(m, cache_pcache0)) upto min(m8, m2), (content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))