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Proof step 9 from proof synced-dirs-add-new-clean-inode (previous step)

pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), icache[ino0] = mkientry(boolvar0, inode0), ino0 ∈ dirs, ino ∈ dirs → (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ icache[ino, mkientry(false, inode)][ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

User applied rule all left

And obtained the following new goals

Proof step 10:
icache[ino0] = mkientry(boolvar0, inode0), pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), ino0 ∈ dirs, ino ∈ dirs → (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ino0 ∈ dirs → (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ icache[ino, mkientry(false, inode)][ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty), ∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ icache[ino, mkientry(false, inode)][ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

Rule argument

pos: left 5 terms: ino0 abort: F discard: F computed: T

Additional information

Used terms: ino0