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Proof step 1332 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = cache_files[m].nlink

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 1333:
# buf-opt0.buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), cache_files[m] = mkfile(m2, md, m3, content0), buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ 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_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = m3

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [cache_files[m], m2, md, m3, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: cache_files[m], m2, md, m3, content0