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Proof step 20 from proof synced-dirs-variant1 (previous step)

pcache[datakey(ino, n0)] = mkpentry(boolvar1, buf0), icache0[ino] = mkientry(boolvar0, inode), pcache0[datakey(ino, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar2, inode0), datakey(ino, n) ∈ pcache0, ino ∈ dirs0, ino ∈ dirs → (ino ∈ icache → ¬ boolvar2) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ino ∈ icache0 → ¬ boolvar0, ∀ 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), ∀ ino. ino ∈ dirs → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].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: left 7

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