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Proof step 2 from proof synced-files-update-clean-inode (previous step)

ino ∈ icache ⊦ synced(files, icache[ino, mkientry(false, inode)], pcache) ↔ synced(files, icache, pcache), icache[ino].dirty

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
icache[ino] = mkientry(boolvar, inode0), ¬ boolvar, ino ∈ icache ⊦ synced(files, icache[ino, mkientry(false, inode)], pcache) ↔ synced(files, icache, pcache)

Rule argument

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

Additional information

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