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Proof step 14 from proof refine-fsync (previous step)

cache_icache[m].inode.ino = m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), (cache_icache[m].dirty ⊃ cache_icache[m].inode.nlink = cache_files[m].nlink ∧ cache_icache[m].inode.nsubdirs = 0 ∧ ¬ cache_icache[m].inode.directory ;cache_icache[m].inode = mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) ⊦ m1 = cache_files[m].nlink

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
cache_icache[m].inode = mkinode(m2, md, boolvar, m3, m4, m5), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), m2 = m, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), (cache_icache[m].dirty ⊃ m3 = cache_files[m].nlink ∧ m4 = 0 ∧ ¬ boolvar ;cache_icache[m].inode = mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ) ⊦ m1 = cache_files[m].nlink

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, m2, md, boolvar, m3, m4, m5]

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, m2, md, boolvar, m3, m4, m5