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Proof step 1192 from proof refine-truncate-buff-none-uncached (previous step)

cache_files[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content), cache_icache[ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m11, m12)), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), ino = m3, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, 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

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1193:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 1194:
cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m11, m12)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), 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? ⊦ ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))), 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), ino ∈ cache_icache ∧ ¬ cache_icache[ino].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s) Used terms: ino, cache_icache, cache_files ⊕ cache_pcache0