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M ? ? v ?(a 1 ,0) (notice that c 2 T also assigns ?(a 1 , 0) But since it just propagates r-values of L L (a 1 ) ? pc which are already propagated by c 0 T , the value of ?(a 1 , 0) keeps being equal ,
Proof: Since ?(x, 0) in not modified by T [a 1 = a 2 , pc]. a 1 = a 2 modifies only locations in Loc(P ). c 2 T do not modify ?(x, 0) since E(x) / ? S P (a 1 = a 2 ). c 1 T modifies only pointers and ?(x, 0) is not ,
Proof: Since assignment pc ? does not modify neither locations in Loc(P ) nor locations associated to shadow variables defined by Additionally, pc ? = s a ? pc where s a is the result of r-value evaluation of a in ,