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Proof step 7 from proof synced-dirs-variant1 (previous step)

pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), icache0[ino] = mkientry(boolvar0, inode), ino ∈ dirs0, ∀ ino. ino ∈ dirs → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[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) ⊦ (ino ∈ icache0 → ¬ boolvar0) ∧ (datakey(ino, n) ∈ pcache0 → ¬ boolvar)

User applied rule all left

And obtained the following new goals

Proof step 8:
icache0[ino] = mkientry(boolvar0, inode), pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), ino ∈ dirs0, (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)) → 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 ∈ icache0 → ¬ boolvar0) ∧ (datakey(ino, n) ∈ pcache0 → ¬ boolvar)

Rule argument

pos: left 5 terms: ino abort: F discard: F computed: T

Additional information

Used terms: ino