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Proof step 53 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf1), 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_icache[m].inode.directory, 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 54:
# buf0 = VFS_PAGE_SIZE, cache_icache[m].inode = mkinode(m0, md, boolvar, m1, m2, m3), cache_pcache[datakey(m, pageno)] = mkpentry(boolvar0, buf1), ¬ boolvar, 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 ∈ cache_files[m].content ⊕ mkcontent(m, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (buf1 = buf0 ∧ ESUCCESS = err), buf1 = (cache_files[m].content ⊕ mkcontent(m, cache_pcache))[pageno]

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache[m].inode, m0, md, boolvar, m1, m2, m3]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache[m].inode, m0, md, boolvar, m1, m2, m3