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Proof step 9 from proof synced-dirs-variant1 (previous step)

icache0[ino] = mkientry(boolvar0, inode), pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), ino ∈ dirs0, (ino ∈ dirs → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (datakey(ino, n0) ∈ pcache → ¬ pcache[datakey(ino, n0)].dirty)) → (ino ∈ icache0 → ¬ boolvar0) ∧ (∀ 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(ino, n0)], boolvar1, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, n0)], boolvar1, buf0