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Proof step 1035 from proof refine-truncate-buff-none-uncached (previous step)

cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))][ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), 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 ⊃ mkfile(m6, md1, # links(m3, cache_dirs), content0 upto min(m6, m2));((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino]) = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0))[ino], datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))], ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))] ∧ boolvar, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))] ∧ ¬ boolvar, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1036:
((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), 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), ino ∈ cache_files, m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino = m3, mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache0)) = mkfile (cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, ino ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)