Expression of type ExprTuple

from the theory of proveit.numbers.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, ExprTuple, IndexedVar, Lambda, Variable, a, b, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_i, b_1_to_j], Conditional(Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j)))))

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(\left(a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{i} + 0+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{i}+ b_{1} +  b_{2} +  \ldots +  b_{j}\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{i} \in \mathbb{C}\right), \left(b_{1} \in \mathbb{C}\right) ,  \left(b_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(b_{j} \in \mathbb{C}\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 15 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprRange	lambda_map: 16 start_index: 26 end_index: 24
12	ExprRange	lambda_map: 17 start_index: 26 end_index: 27
13	ExprTuple	19, 18, 20
14	Literal
15	ExprTuple	19, 20
16	Lambda	parameter: 37 body: 21
17	Lambda	parameter: 37 body: 22
18	Literal
19	ExprRange	lambda_map: 23 start_index: 26 end_index: 24
20	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
21	Operation	operator: 29 operands: 28
22	Operation	operator: 29 operands: 30
23	Lambda	parameter: 37 body: 31
24	Variable
25	Lambda	parameter: 37 body: 32
26	Literal
27	Variable
28	ExprTuple	31, 33
29	Literal
30	ExprTuple	32, 33
31	IndexedVar	variable: 34 index: 37
32	IndexedVar	variable: 35 index: 37
33	Literal
34	Variable
35	Variable
36	ExprTuple	37
37	Variable