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Proof step 462 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, content[pageno] = zeropage, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), 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), pageno ∈ content, m ∈ cache_files, ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err)⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), ⟨if pageno ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content then buf0 := ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].content[pageno] else buf0 := zeropage; err := ESUCCESS⟩ (content[pageno] = buf0 ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 463:
# buf0 = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), content[pageno] = zeropage, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content0), 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, pageno ∈ content, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err)⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), ⟨if pageno ∈ content0 then buf0 := content0[pageno] else buf0 := zeropage; err := ESUCCESS⟩ (content[pageno] = buf0 ∧ ESUCCESS = err), datakey(m, pageno) ∈ cache_pcache

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, 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 ⊕ cache_pcache) ⊕ cache_icache)[m], m0, md, m1, content0