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Proof step 48 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf1), cache_icache[m] = mkientry(boolvar1, mkinode(m2, md0, true, m3, m4, m5)), buf1 ≠ (cache_files[m].content ⊕ mkcontent(m, cache_pcache))[pageno], 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), pageno ∈ cache_files[m].content ⊕ mkcontent(m, cache_pcache), m ∈ cache_files, datakey(m, pageno) ∈ cache_pcache, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (buf1 = buf0 ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 49:
# buf0 = VFS_PAGE_SIZE, cache_icache[m] = mkientry(boolvar1, mkinode(m2, md0, true, m3, m4, m5)), cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf1), cache_files[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_icache, datakey(m, pageno) ∈ cache_pcache, m ∈ cache_files, pageno ∈ content ⊕ mkcontent(m, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (buf1 = buf0 ∧ ESUCCESS = err), buf1 = (content ⊕ mkcontent(m, cache_pcache))[pageno]

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], 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[m], m0, md, m1, content