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Proof step 25 from proof synced-files-variant1 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
icache[ino] = mkientry(boolvar0, inode), pcache0[datakey(ino, n)] = mkpentry(boolvar, buf), icache0[ino] = mkientry(boolvar1, inode0), ino ∈ files0, ino ∈ files → (ino ∈ icache → ¬ boolvar0) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty), ∀ ino. ino ∈ files0 → (ino ∈ icache0 → ¬ icache0[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty), ∀ ino. ino ∈ files → (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty) ⊦ (ino ∈ icache0 → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 → ¬ boolvar)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache0[ino], boolvar1, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache0[ino], boolvar1, inode0