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Proof step 57 from proof refine-iget (previous step)

err = ESUCCESS, inode = inode0, 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 ⊦ ⟪afs_iget#(ino, cache_dirs, cache_files, cache_asynced; inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then icache_set#(inode, false; err, cache_icache)⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ inode = inode0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 58:
asynced ↔ cache_asynced, dirs = cache_dirs, err = ESUCCESS, files = cache_files, inode = inode0, 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 ⊦ ⟪if pre-iget(ino, dirs, files) then {{inode := getinode(ino, dirs, files); err := ESUCCESS} or fail#(; ; err)} else abort; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then icache_set#(inode, false; err, cache_icache)⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ inode = inode0 ∧ err = err0), ino ∈ cache_icache

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_iget#(INO, DIRS, FILES, ASYNCED; INODE, ERR) {if pre-iget(INO, DIRS, FILES) then { {INODE := getinode(INO, DIRS, FILES); ERR := ESUCCESS} or fail#(; ; ERR)} else abort };