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

inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode.ino].nlink, inode.nsubdirs = 0, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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, ¬ inode.directory, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_fsync#(inode, asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)⟫ ⟨afs_fsync#(inode, asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, ¬ boolvar, inode = mkinode(m, md, boolvar, m0, m1, m2), m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, m1 = 0, 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_fsync#(inode, asynced, cache_sync; cache_dirs, cache_files, cache_icache, cache_pcache, cache_asynced; err)⟫ ⟨afs_fsync#(inode, asynced, afs_dirs, afs_files; ; afs_asynced, err0)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ 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