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Proof step 78 from proof refine-writepage (previous step)

# buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content:= ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content[pageno, buf] ] ≠ (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache, 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 ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 79:
# buf = VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content), 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 ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ( (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content:= content[pageno, buf]] = (cache_files ⊕ cache_pcache[datakey(m, pageno), mkpentry(true, buf)]) ⊕ cache_icache

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 ⊕ cache_pcache) ⊕ cache_icache)[m], m0, md, m1, content]

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 ⊕ cache_pcache) ⊕ cache_icache)[m], m0, md, m1, content