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Proof step 232 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, true, m4, m5, m6)), (∅)[ino] = mkientry(boolvar1, mkinode(m0, md, boolvar, m1, m7, m8)), 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 ∈ content ⊕ mkcontent(m, cache_pcache), ino ∈ cache_files, m ∈ cache_icache, m ∈ cache_files, pageno ∈ content, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content[pageno] = zeropage, mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)) = mkfile (cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])])), ino ∈ cache_icache, datakey(m, pageno) ∈ cache_pcache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 233:
# buf0 = VFS_PAGE_SIZE, (∅)[ino] = mkientry(boolvar1, mkinode(m0, md, boolvar, m1, m7, m8)), cache_icache[m] = mkientry(boolvar0, mkinode(m2, md1, true, m4, m5, m6)), cache_files[m] = mkfile(m3, md0, # links(m, cache_dirs), content), content[pageno] = (content ⊕ mkcontent(m, cache_pcache))[pageno], cache_files[ino] = mkfile(m9, md2, m10, content0), 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, m ∈ cache_icache, ino ∈ cache_files, pageno ∈ content ⊕ mkcontent(m, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ content[pageno] = zeropage, mkfile(m9, md2, m10, content0 ⊕ mkcontent(ino, cache_pcache)) = mkfile(m9, md2, m10, content0 ⊕ mkcontent(ino, cache_pcache[datakey(m, pageno), mkpentry(false, content[pageno])])), datakey(m, pageno) ∈ cache_pcache, ino ∈ 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[ino], m9, md2, m10, 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[ino], m9, md2, m10, content0