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Proof step 2 from proof inv-iget (previous step)

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-iget(ino, dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_iget#(ino, dirs, files, asynced0; inode, err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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 ⊦ ⟪cache_iget#(ino, dirs, files, asynced0; inode, err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Rule argument

Additional information

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