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Proof step 17 from proof synced-files-variant1 (previous step)

icache[ino] = mkientry(boolvar2, inode0), pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), icache0[ino] = mkientry(boolvar0, inode), pcache[datakey(ino, n0)] = mkpentry(boolvar1, buf0), ino ∈ files0, ino ∈ icache → ¬ boolvar2, (ino ∈ files → datakey(ino, n0) ∈ pcache → ¬ boolvar1) → (ino ∈ icache0 → ¬ boolvar0) ∧ (∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ ino. ino ∈ files → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ ino. (ino ∈ files → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)) → ino ∈ files0 → (ino ∈ icache0 → ¬ icache0[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty) ⊦ (ino ∈ icache0 → ¬ boolvar0) ∧ (datakey(ino, n) ∈ pcache0 → ¬ boolvar)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 7

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