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Proof step 4 from proof overwrite-write-inode-clean-dir (previous step)

icache[ino].inode = mkinode(m, md0, true, m0, m1, m2), ino ∈ icache, ino ∈ dirs ⊦ (files ⊕ pcache) ⊕ icache = (files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
icache[ino] = mkientry(boolvar, inode), inode = mkinode(m, md0, true, m0, m1, m2), ino ∈ dirs, ino ∈ icache ⊦ (files ⊕ pcache) ⊕ icache = (files ⊕ pcache) ⊕ icache[ino, mkientry(false, mkinode(m, md, true, m0, m1, m2))]

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, inode]

Additional information

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