proposition: Lemma evalRealizeStateAux2 : forall (A : Prop) (f : rNat -> bool) (p q r s : rZ) (S : State) (EqS : eqStateRz S p q), (rZEval f p = rZEval f q /\ rZEval f r = rZEval f s -> A) -> realizeState f (addEq (r, s) S) -> A.
proof: Proof. intros A f p q r s S H' H'0 H'1. lapply H'0; [ intros H'2 | split ]; auto with stalmarck. apply realizeStateInv with (S := S); auto with stalmarck. apply realizeStateIncl with (1 := H'1); auto with stalmarck. apply realizeStateInv with (1 := H'1); auto with stalmarck. Qed.