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Proof step 11 from proof overwrite-write-inode-dirty (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
icache[ino] = mkientry(boolvar, inode), ino ∈ icache, ino ∈ files ⊦ (((files ⊕ pcache) ⊕ icache)[ino].meta:= md).size:= m = ((files ⊕ pcache) ⊕ icache[ino, mkientry(true, (inode.meta:= md).size:= m)])[ino], inode.directory

Rule argument

Additional information

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