# from the theory of proveit.numbers.addition¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, IndexedVar, Lambda, Variable, a, i
from proveit.core_expr_types import a_1_to_i
from proveit.logic import And, InSet
from proveit.numbers import Add, Complex, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_i], Conditional(InSet(Add(a_1_to_i), Complex), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i))))

expr:
In [3]:
# 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")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a_{1}, a_{2}, \ldots, a_{i}\right) \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \in \mathbb{C} \textrm{ if } \left(a_{1} \in \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{C}\right)\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 10
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 17
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 20
5Literal
6ExprTuple8
7Operationoperator: 9
operands: 10
8ExprRangelambda_map: 11
start_index: 15
end_index: 16
9Literal
10ExprTuple12
11Lambdaparameter: 23
body: 13
12ExprRangelambda_map: 14
start_index: 15
end_index: 16
13Operationoperator: 17
operands: 18
14Lambdaparameter: 23
body: 19
15Literal
16Variable
17Literal
18ExprTuple19, 20
19IndexedVarvariable: 21
index: 23
20Literal
21Variable
22ExprTuple23
23Variable