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Proof step 2 from proof overwrite-write-inode-dirty (previous step)

ino ∈ files, ino ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino, (((files ⊕ pcache) ⊕ icache)[ino].meta:= md).size:= m] = (files ⊕ pcache) ⊕ icache[ino, mkientry(true, (icache[ino].inode.meta:= md).size:= m)], icache[ino].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
icache[ino] = mkientry(boolvar, inode), ino ∈ icache, ino ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino, (((files ⊕ pcache) ⊕ icache)[ino].meta:= md).size:= m] = (files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)], inode.directory

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