import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, ExprTuple, Function, IndexedVar, Lambda, P, Px, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, FALSE, Forall, InSet, Or, Set
from proveit.numbers import Natural, one
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Equals(Or(ExprRange(sub_expr1, Equals(Function(P, [IndexedVar(a, sub_expr1)]), FALSE), one, n)), Equals(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), FALSE)))), InSet(n, Natural))))
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()