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Proof step 1052 from proof refine-truncate-buff-none-uncached (previous step)

cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), ((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)), cache_icache[m3] = mkientry(boolvar2, mkinode(m9, md3, boolvar1, m10, 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), ino ∈ cache_files, m3 ∈ cache_files, 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, ino ∈ cache_icache, (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, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ cache_icache ∧ ¬ boolvar1, m3 ∈ cache_icache ∧ boolvar1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1053:
⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]
Proof step 1054:
cache_icache[m3] = mkientry(boolvar2, mkinode(m9, md3, boolvar1, m10, m11, m12)), (∅)[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)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), 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, ino ∈ cache_icache, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m3 ∈ cache_icache, m3 ∈ cache_icache ∧ boolvar1, m3 ∈ cache_icache ∧ ¬ boolvar1, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, (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])

Rule argument

spec: cache-base name: at-icache-overwrite-not-cached seq: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [m3, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used terms: m3, cache_icache, cache_files ⊕ cache_pcache0