Expression of type ExprTuple

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 ExprTuple, Lambda, Q, f, j, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall
from proveit.numbers import Complex, NaturalPos
from proveit.numbers.summation import summation_b1toj_fQ

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, Q], Forall(instance_param_or_params = [n, j], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(vec_summation_b1toj_fQ, summation_b1toj_fQ), domain = Complex), domain = NaturalPos)))

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(f, Q\right) \mapsto \left[\forall_{n, j \in \mathbb{N}^+}~\left[\forall_{x_{1}, x_{2}, \ldots, x_{n} \in \mathbb{C}}~\left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\right)\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: 2 body: 3
2	ExprTuple	46, 47
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	36, 53
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 27 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15
13	Lambda	parameters: 16 body: 17
14	Operation	operator: 40 operands: 18
15	Operation	operator: 40 operands: 19
16	ExprTuple	20
17	Conditional	value: 21 condition: 22
18	ExprTuple	36, 23
19	ExprTuple	53, 23
20	ExprRange	lambda_map: 24 start_index: 52 end_index: 36
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Lambda	parameter: 57 body: 44
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31
29	Operation	operator: 32 operand: 37
30	Operation	operator: 33 operand: 37
31	ExprRange	lambda_map: 35 start_index: 52 end_index: 36
32	Literal
33	Literal
34	ExprTuple	37
35	Lambda	parameter: 57 body: 38
36	Variable
37	Lambda	parameters: 48 body: 39
38	Operation	operator: 40 operands: 41
39	Conditional	value: 42 condition: 43
40	Literal
41	ExprTuple	44, 45
42	Operation	operator: 46 operands: 48
43	Operation	operator: 47 operands: 48
44	IndexedVar	variable: 49 index: 57
45	Literal
46	Variable
47	Variable
48	ExprTuple	50
49	Variable
50	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
51	Lambda	parameter: 57 body: 54
52	Literal
53	Variable
54	IndexedVar	variable: 55 index: 57
55	Variable
56	ExprTuple	57
57	Variable