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Proof step 23 from proof synced-dirs-add-new-clean-inode (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
pcache[datakey(ino0, n)] = mkpentry(boolvar, buf), icache[ino, mkientry(false, inode)][ino0] = mkientry(boolvar0, inode0), ino0 ∈ dirs, ∀ ino0. ino0 ∈ dirs → (ino0 ∈ icache → ¬ icache[ino0].dirty) ∧ (∀ n. datakey(ino0, n) ∈ pcache → ¬ pcache[datakey(ino0, n)].dirty) ⊦ ino ∈ icache, (ino0 ∈ icache[ino, mkientry(false, inode)] → ¬ boolvar0) ∧ (datakey(ino0, n) ∈ pcache → ¬ boolvar)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino, mkientry(false, inode)][ino0], boolvar0, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino, mkientry(false, inode)][ino0], boolvar0, inode0