Expression of type Lambda

from the theory of proveit.linear_algebra.addition

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, IndexedVar, Lambda, Variable, a, i
from proveit.core_expr_types import a_1_to_i
from proveit.linear_algebra import VecAdd
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, one

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

expr:

# 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

# 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) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}\right) \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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operands: 13
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
11	Literal
12	Literal
13	ExprTuple	15
14	Lambda	parameter: 26 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 26 body: 22
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	IndexedVar	variable: 24 index: 26
23	Literal
24	Variable
25	ExprTuple	26
26	Variable