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Proof step 3 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf = buf0, err = err0, 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), inode.ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_readpage#(inode, pageno, cache_dirs, cache_files, cache_asynced; buf, err, cache_pcache)⟫ ⟨afs_readpage#(inode, pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ buf = buf0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# buf0 = VFS_PAGE_SIZE, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf = buf0, err = err0, inode = mkinode(m, md, boolvar, m0, m1, m2), 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_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_readpage#(inode, pageno, cache_dirs, cache_files, cache_asynced; buf, err, cache_pcache)⟫ ⟨afs_readpage#(inode, pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ buf = buf0 ∧ err = err0)

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] → [inode, m, md, boolvar, m0, m1, m2]

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: inode, m, md, boolvar, m0, m1, m2