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Proof step 1167 from proof refine-truncate-buff-none-uncached (previous step)

cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), cache_icache[m3] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), cache_files[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content), 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), m3 ∈ cache_icache, ino ∈ cache_files, m3 ∈ cache_files, ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m3, cache_pcache0), (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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 1168:
cache_files[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content), cache_icache[m3] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), cache_icache[ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), 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), ino ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_files, m3 ∈ cache_icache, n ∈ content ⊕ mkcontent(ino, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, (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]), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m3, cache_pcache0), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Rule argument

fma: n ∈ content ⊕ mkcontent(ino, cache_pcache0)

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)%⊦ key ∈ truncate(ino, size, pcache) ↔ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino); (s)% ⊦ datakey(m, m0).data?; (s) Used formulas: n ∈ content ⊕ mkcontent(ino, cache_pcache0)