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, ExprTuple, Lambda, i, j
from proveit.core_expr_types import a_1_to_i, b_1_to_j
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Complex, Natural, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_j], instance_expr = Equals(Add(a_1_to_i, zero, b_1_to_j), Add(a_1_to_i, b_1_to_j)), domain = Complex), And(InSet(i, Natural), InSet(j, Natural)))))

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(i, j\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\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)\right) \textrm{ if } i \in \mathbb{N} ,  j \in \mathbb{N}\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: 2 body: 3
2	ExprTuple	37, 40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 28 body: 12
10	Operation	operator: 42 operands: 13
11	Operation	operator: 42 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	37, 17
14	ExprTuple	40, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 27 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprRange	lambda_map: 29 start_index: 39 end_index: 37
25	ExprRange	lambda_map: 30 start_index: 39 end_index: 40
26	ExprTuple	32, 31, 33
27	Literal
28	ExprTuple	32, 33
29	Lambda	parameter: 50 body: 34
30	Lambda	parameter: 50 body: 35
31	Literal
32	ExprRange	lambda_map: 36 start_index: 39 end_index: 37
33	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
34	Operation	operator: 42 operands: 41
35	Operation	operator: 42 operands: 43
36	Lambda	parameter: 50 body: 44
37	Variable
38	Lambda	parameter: 50 body: 45
39	Literal
40	Variable
41	ExprTuple	44, 46
42	Literal
43	ExprTuple	45, 46
44	IndexedVar	variable: 47 index: 50
45	IndexedVar	variable: 48 index: 50
46	Literal
47	Variable
48	Variable
49	ExprTuple	50
50	Variable