Expression of type Lambda

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, 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 32 body: 2
1	ExprTuple	32
2	Operation	operator: 3 operand: 5
3	Literal
4	ExprTuple	5
5	Lambda	parameters: 39 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 18 operand: 22
14	Operation	operator: 18 operand: 23
15	Operation	operator: 34 operands: 20
16	Operation	operator: 34 operands: 21
17	ExprTuple	22
18	Literal
19	ExprTuple	23
20	ExprTuple	50, 24
21	ExprTuple	49, 24
22	Lambda	parameter: 43 body: 25
23	Lambda	parameter: 43 body: 26
24	Literal
25	Conditional	value: 27 condition: 28
26	Conditional	value: 29 condition: 30
27	Operation	operator: 32 operand: 43
28	Operation	operator: 34 operands: 31
29	Operation	operator: 32 operand: 37
30	Operation	operator: 34 operands: 35
31	ExprTuple	43, 36
32	Variable
33	ExprTuple	37
34	Literal
35	ExprTuple	43, 38
36	Operation	operator: 41 operands: 39
37	Operation	operator: 47 operand: 43
38	Operation	operator: 41 operands: 42
39	ExprTuple	50, 49
40	ExprTuple	43
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Operation	operator: 47 operand: 49
45	Operation	operator: 47 operand: 50
46	ExprTuple	49
47	Literal
48	ExprTuple	50
49	Variable
50	Variable