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Proof step 65 from proof refine-iget (previous step)

afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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), ¬ ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟪icache_set# ((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) ), false ; err, cache_icache)⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ ( afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (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)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 66:
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 ⊕ 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 ⊦ ⟪icache[inode.ino] := mkientry(asynced, inode)⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ ( afs_files = (cache_files ⊕ cache_pcache) ⊕ icache ∧ (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

pos: right 1

Additional information

Used simplifier rules: icache_set#(INODE, DIRTY; ERR, ICACHE) {ICACHE[INODE.ino] := mkientry(DIRTY, INODE)};