import proveit from proveit import ExprTuple from proveit import a, b, c, x from proveit.logic import in_bool, InSet, CartExp from proveit.numbers import Real, three %begin demonstrations
x_in_R3_def = InSet(x, CartExp(Real, three)).definition()
x_in_R3_def.lhs.unfold(assumptions=[x_in_R3_def.lhs])
x_in_R3_def.lhs.fold(assumptions=[x_in_R3_def.rhs])
x_in_R3_def.lhs.prove(assumptions=[x_in_R3_def.rhs])
in_bool(x_in_R3_def.lhs).prove()
abc = ExprTuple(a, b, c)
abc_in_R3_def = InSet(abc, CartExp(Real, three)).definition()
abc_in_R3_def.lhs.unfold(assumptions=[abc_in_R3_def.lhs])
abc_in_R3_def.lhs.fold(assumptions=[abc_in_R3_def.rhs])
abc_in_R3_def.lhs.prove(assumptions=[abc_in_R3_def.rhs])
in_bool(abc_in_R3_def.lhs).prove()
%end demonstrations