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Proof step 19 from proof inv-iget (previous step)

asynced ↔ asynced1, 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), asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ⟪if pre-iget(ino, dirs, files) then {{inode := getinode(ino, dirs, files); err := ESUCCESS} or fail#(; ; err)} else abort; if err = ESUCCESS then icache_set#(inode, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), ino ∈ icache

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 20:
asynced ↔ asynced1, 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), asynced2 → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ⟪{inode := getinode(ino, dirs, files); err := ESUCCESS} or fail#(; ; err); if err = ESUCCESS then icache_set#(inode, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache))), ino ∈ icache

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)