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Proof step 1141 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_icache[m] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), cache_pcache0[datakey(m, n)] = mkpentry(boolvar, buf), buf-opt0.some?, n * VFS_PAGE_SIZE < min(m8, m2), 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), n ∈ content1 ⊕ mkcontent(m, cache_pcache0), m ∈ cache_files, m ∈ cache_icache, datakey(m, n) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ buf = truncate(m, min(m8, m2), cache_pcache0)[datakey(m, n)].page, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1142:
# buf-opt0.buf = VFS_PAGE_SIZE, cache_pcache0[datakey(m, n)] = mkpentry(boolvar, buf), cache_icache[m] = mkientry(boolvar1, mkinode(m10, md4, true, m11, m12, m13)), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), truncate(m, min(m8, m2), cache_pcache0)[datakey(m, n)] = mkpentry(boolvar0, buf0), buf-opt0.some?, n * VFS_PAGE_SIZE < min(m8, m2), 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), datakey(m, n) ∈ cache_pcache0, m ∈ cache_icache, m ∈ cache_files, n ∈ content1 ⊕ mkcontent(m, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ buf = buf0, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [truncate(m, min(m8, m2), cache_pcache0)[datakey(m, n)], boolvar0, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: truncate(m, min(m8, m2), cache_pcache0)[datakey(m, n)], boolvar0, buf0