Expression of type ExprTuple

from the theory of proveit.numbers.summation

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, Function, Lambda, a, b, f, fx, x
from proveit.logic import Equals, Forall
from proveit.numbers import Integer, Interval, Neg, Sum

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(f, Forall(instance_param_or_params = [a, b], instance_expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = Function(f, [Neg(x)]), domain = Interval(Neg(b), Neg(a)))), domain = Integer)))

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(f \mapsto \left[\forall_{a, b \in \mathbb{Z}}~\left(\left(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\sum_{x = -b}^{-a} f\left(-x\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	parameter: 33 body: 3
2	ExprTuple	33
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameters: 40 body: 7
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 19 operand: 23
15	Operation	operator: 19 operand: 24
16	Operation	operator: 35 operands: 21
17	Operation	operator: 35 operands: 22
18	ExprTuple	23
19	Literal
20	ExprTuple	24
21	ExprTuple	51, 25
22	ExprTuple	50, 25
23	Lambda	parameter: 44 body: 26
24	Lambda	parameter: 44 body: 27
25	Literal
26	Conditional	value: 28 condition: 29
27	Conditional	value: 30 condition: 31
28	Operation	operator: 33 operand: 44
29	Operation	operator: 35 operands: 32
30	Operation	operator: 33 operand: 38
31	Operation	operator: 35 operands: 36
32	ExprTuple	44, 37
33	Variable
34	ExprTuple	38
35	Literal
36	ExprTuple	44, 39
37	Operation	operator: 42 operands: 40
38	Operation	operator: 48 operand: 44
39	Operation	operator: 42 operands: 43
40	ExprTuple	51, 50
41	ExprTuple	44
42	Literal
43	ExprTuple	45, 46
44	Variable
45	Operation	operator: 48 operand: 50
46	Operation	operator: 48 operand: 51
47	ExprTuple	50
48	Literal
49	ExprTuple	51
50	Variable
51	Variable