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Proof step 3 from proof synced-dirs-variant1 (previous step)

∀ ino. ino ∈ dirs → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty) ⊦ ¬(∀ ino. ino ∈ dirs0 → (ino ∈ icache0 → ¬ icache0[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty)) ↔ ¬ (∀ ino. (ino ∈ dirs → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)) → ino ∈ dirs0 → (ino ∈ icache0 → ¬ icache0[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

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