Expression of type Forall

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 Function, 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 = 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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 37 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 16 operand: 20
12	Operation	operator: 16 operand: 21
13	Operation	operator: 32 operands: 18
14	Operation	operator: 32 operands: 19
15	ExprTuple	20
16	Literal
17	ExprTuple	21
18	ExprTuple	48, 22
19	ExprTuple	47, 22
20	Lambda	parameter: 41 body: 23
21	Lambda	parameter: 41 body: 24
22	Literal
23	Conditional	value: 25 condition: 26
24	Conditional	value: 27 condition: 28
25	Operation	operator: 30 operand: 41
26	Operation	operator: 32 operands: 29
27	Operation	operator: 30 operand: 35
28	Operation	operator: 32 operands: 33
29	ExprTuple	41, 34
30	Variable
31	ExprTuple	35
32	Literal
33	ExprTuple	41, 36
34	Operation	operator: 39 operands: 37
35	Operation	operator: 45 operand: 41
36	Operation	operator: 39 operands: 40
37	ExprTuple	48, 47
38	ExprTuple	41
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Operation	operator: 45 operand: 47
43	Operation	operator: 45 operand: 48
44	ExprTuple	47
45	Literal
46	ExprTuple	48
47	Variable
48	Variable