Expression of type Equals

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 a, b, fb, fx, x
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, b)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, subtract(b, one))), fb))

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(\sum_{x = a}^{b} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b - 1} f\left(x\right)\right) + f\left(b\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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