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

afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, 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 ⊦ ⟪cache_iget#(ino, cache_dirs, cache_files, cache_asynced; inode, 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)

User applied rule call right

And obtained the following new goals

Proof step 4:
asynced1 ↔ cache_asynced, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ⟪if pre-iget(ino, dirs, files) then let asynced0 = false, asynced = false in {icache_get#(ino, icache; asynced0, inode, err); if ¬ asynced0 ∨ err ≠ ESUCCESS then {afs_iget#(ino, dirs, files, asynced1; inode, err); if err = ESUCCESS then icache_set#(inode, asynced; err, icache)}} else abort⟫ ⟨afs_iget#(ino, cache_dirs, afs_files, cache_asynced; inode0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ icache ∧ inode = inode0 ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: cache_iget#(INO, DIRS, FILES, ASYNCED; INODE, ERR, ICACHE) {if pre-iget(INO, DIRS, FILES) then let HIT = false, DIRTY = false in {icache_get#(INO, ICACHE; HIT, INODE, ERR); if ¬ HIT ∨ ERR ≠ ESUCCESS then {afs_iget#(INO, DIRS, FILES, ASYNCED; INODE, ERR); if ERR = ESUCCESS then icache_set#(INODE, DIRTY; ERR, ICACHE)}} else abort };