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Proof step 4 from proof inv-iget (previous step)

asynced1 ↔ asynced0, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ 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⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 5:
asynced1 ↔ asynced0, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache), ino ∈ dirs ∨ ino ∈ files ⊦ ⟪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)}}⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

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)