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Proof step 9 from proof refine-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, ¬ asynced0, buf = buf0, err = err0, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪pcache_get#(m, pageno, cache_pcache; asynced0, buf, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if ¬ asynced0 ∨ err ≠ ESUCCESS then {afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, cache_files, cache_asynced; buf, err); if err = ESUCCESS ∧ buf ≠ zeropage then let asynced = false in pcache_set#(m, pageno, buf, asynced; err, cache_pcache)}⟫ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ buf = buf0 ∧ err = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 10:
# buf0 = VFS_PAGE_SIZE, asynced ↔ asynced0, ¬ asynced0, buf = buf0, err = err0, ino = m, pcache = cache_pcache, 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), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪let key = datakey(ino, pageno) in if key ∈ pcache then let pe = pcache[key] in {buf := pe.page; asynced := true} else asynced := false; err := ESUCCESS; afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if ¬ asynced ∨ err ≠ ESUCCESS then {afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, cache_files, cache_asynced; buf, err); if err = ESUCCESS ∧ buf ≠ zeropage then let asynced = false in pcache_set#(m, pageno, buf, asynced; err, cache_pcache)}⟫ ⟨afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), pageno, cache_dirs, afs_files, cache_asynced; buf0, err0)⟩ (afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ buf = buf0 ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: pcache_get#(INO, PAGENO, PCACHE; HIT, BUF, ERR) {let KEY = datakey(INO, PAGENO) in if KEY ∈ PCACHE then let PE = PCACHE[KEY] in {BUF := PE.page; HIT := true} else HIT := false; ERR := ESUCCESS };