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Proof step 8 from proof synced-dirs-add-new-clean-inode (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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)

Rule argument

Additional information

Used simplifier rules: ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino, ie]; (s)