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 A, ExprRange, ExprTuple, IndexedVar, Variable, m, n
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet, Or
from proveit.numbers import Add, NaturalPos, one, two
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, one)
sub_expr3 = IndexedVar(A, sub_expr1)
sub_expr4 = Add(m, one)
sub_expr5 = ExprRange(sub_expr1, sub_expr3, one, n)
expr = ExprTuple(And(Forall(instance_param_or_params = [sub_expr2], instance_expr = InSet(sub_expr2, Boolean), domain = Boolean), Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr3, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr3, one, sub_expr4)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, sub_expr4)), domain = NaturalPos, condition = Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean))), Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [sub_expr5], instance_expr = InSet(Or(sub_expr5), Boolean), domain = Boolean), domain = NaturalPos))
# 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()