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Proof step 1351 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]) = mkfile(m8, md3, m9, content), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar0, mkinode(m, md, false, m4, m5, m7)), cache_icache[m3] = mkientry(boolvar1, mkinode(m0, md0, false, # links(m3, cache_dirs), m11, m12)), 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, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data?, m2 / VFS_PAGE_SIZE ∈ content1 ∨ m2 / VFS_PAGE_SIZE ∈ mkcontent(m3, cache_pcache0) ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0)) upto min(m6, m2)) ;((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] ) = mkfile(m7, md, m4, content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 ≤ m6, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1352:
# buf0 = VFS_PAGE_SIZE, (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2));cache_files[ino]) = mkfile(m8, md3, m9, content), cache_icache[m3] = mkientry(boolvar1, mkinode(m0, md0, false, # links(m3, cache_dirs), m11, m12)), cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar0, mkinode(m, md, false, m4, m5, m7)), cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), 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, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, ino ∈ cache_files, m3 ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (ino = m3 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), (content1 ⊕ mkcontent(m3, cache_pcache0)) upto min(m6, m2)) ;((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] ) = mkfile(m7, md, m4, content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 ≤ m6

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)