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Proof step 3 from proof inv-lookup (previous step)

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), p_ino ∈ dirs, asynced → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪cache_lookup#(p_ino, dirs, files, asynced0; dent, err, dcache)⟫ dcache-cons(dcache, dirs, files)

User applied rule call right

And obtained the following new goals

Proof step 4:
afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), p_ino ∈ dirs, asynced → synced(files, icache, pcache), links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪if pre-lookup(p_ino, dent, dirs, files) then let asynced = false, name = dent.name in {dcache_get#(p_ino, name, dcache; asynced, dent, err); if ¬ asynced ∨ err ≠ ESUCCESS then {afs_lookup#(p_ino, dirs, files, asynced0; dent, err); if err = ESUCCESS then dcache_set#(p_ino, name, dent; err, dcache)}} else abort⟫ dcache-cons(dcache, dirs, files)

Rule argument

pos: right 1

Additional information

Used simplifier rules: lookup: ⊦ ;