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Proof step 181 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(false, inode), files[m] = mkfile(m1, md, # links(m, dirs), content0), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ ⟪icache_set_status#(m, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 182:
asynced ↔ false, files[m] = mkfile(m1, md, # links(m, dirs), content0), icache[m] = mkientry(false, inode), err = ESUCCESS, ino = m, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache ⊦ ⟪if ino ∈ icache then icache[ino].dirty := asynced else err := EFAIL⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache))

Rule argument

pos: right 1

Additional information

Used simplifier rules: icache_set_status#(INO, DIRTY; ERR, ICACHE) {if INO ∈ ICACHE then ICACHE[INO].dirty := DIRTY else ERR := EFAIL};