/// <summary>
/// Prove <tt>store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))</tt>.
/// </summary>
/// <remarks>This example demonstrates how to use the array theory.</remarks>
public static void ArrayExample2(Context ctx)
{
Console.WriteLine("ArrayExample2");
Sort int_type = ctx.IntSort;
Sort array_type = ctx.MkArraySort(int_type, int_type);
ArrayExpr a1 = (ArrayExpr)ctx.MkConst("a1", array_type);
ArrayExpr a2 = ctx.MkArrayConst("a2", int_type, int_type);
Expr i1 = ctx.MkConst("i1", int_type);
Expr i2 = ctx.MkConst("i2", int_type);
Expr i3 = ctx.MkConst("i3", int_type);
Expr v1 = ctx.MkConst("v1", int_type);
Expr v2 = ctx.MkConst("v2", int_type);
Expr st1 = ctx.MkStore(a1, i1, v1);
Expr st2 = ctx.MkStore(a2, i2, v2);
Expr sel1 = ctx.MkSelect(a1, i3);
Expr sel2 = ctx.MkSelect(a2, i3);
/* create antecedent */
BoolExpr antecedent = ctx.MkEq(st1, st2);
/* create consequent: i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3) */
BoolExpr consequent = ctx.MkOr(new BoolExpr[] { ctx.MkEq(i1, i3), ctx.MkEq(i2, i3), ctx.MkEq(sel1, sel2) });
/* prove store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3)) */
BoolExpr thm = ctx.MkImplies(antecedent, consequent);
Console.WriteLine("prove: store(a1, i1, v1) = store(a2, i2, v2) implies (i1 = i3 or i2 = i3 or select(a1, i3) = select(a2, i3))");
Console.WriteLine("{0}", (thm));
Prove(ctx, thm);
}