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Proof step 90 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, cache_files[m].content[pageno] ≠ zeropage, 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 ∈ cache_files[m].content, ¬ datakey(m, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪pcache_set#(m, pageno, cache_files[m].content[pageno], false; err, cache_pcache)⟫ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ cache_files[m].content[pageno] = buf0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 91:
# buf0 = VFS_PAGE_SIZE, cache_files[m] = mkfile(m3, md0, m4, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪pcache_set#(m, pageno, content[pageno], false; err, cache_pcache)⟫ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ content[pageno] = buf0 ∧ err = err0), content[pageno] = zeropage, 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[m], m3, md0, m4, 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], m3, md0, m4, content