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Proof step 20 from proof overwrite-write-inode-dirty (previous step)

icache[ino] = mkientry(boolvar, inode), ino0 ∈ icache[ino, mkientry(true, (inode.meta:= md).size:= m)], ino0 ∈ files, ino ∈ files, ino ∈ icache, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], ino0 = ino, inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
icache[ino] = mkientry(boolvar, inode), ino ∈ icache, ino ∈ files, ino0 ∈ files, ino0 ∈ icache ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino0], ino0 = ino, inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)