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Proof step 67 from proof refine-iget (previous step)

asynced ↔ false, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, icache = cache_icache, inode = (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size) ), 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ ( afs_files = (cache_files ⊕ cache_pcache) ⊕ icache[inode.ino, mkientry(asynced, inode)] ∧ (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size) ) = inode0 ∧ err = err0), ino ∈ cache_icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 68:
asynced ↔ false, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, icache = cache_icache, inode = (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size) ), inode = mkinode(m, md, boolvar, m0, m1, m2), 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ ( afs_files = (cache_files ⊕ cache_pcache) ⊕ icache[m, mkientry(asynced, inode)] ∧ (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size) ) = inode0 ∧ err = err0), ino ∈ cache_icache

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