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 c, d, fj, gj, j, x
from proveit.logic import Equals
from proveit.numbers import Interval, Mult, Sum

# build up the expression from sub-expressions
sub_expr1 = [j]
sub_expr2 = Interval(c, d)
expr = Equals(Sum(index_or_indices = sub_expr1, summand = Mult(Mult(x, gj), fj), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = Mult(gj, fj), domain = sub_expr2)))

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_{j = c}^{d} \left(\left(x \cdot g\left(j\right)\right) \cdot f\left(j\right)\right)\right) = \left(x \cdot \left(\sum_{j = c}^{d} \left(g\left(j\right) \cdot f\left(j\right)\right)\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: 10 operand: 7
4	Operation	operator: 20 operands: 6
5	ExprTuple	7
6	ExprTuple	24, 8
7	Lambda	parameter: 33 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 12 condition: 18
10	Literal
11	ExprTuple	13
12	Operation	operator: 20 operands: 14
13	Lambda	parameter: 33 body: 15
14	ExprTuple	16, 26
15	Conditional	value: 17 condition: 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 25
20	Literal
21	ExprTuple	25, 26
22	Literal
23	ExprTuple	33, 27
24	Variable
25	Operation	operator: 28 operand: 33
26	Operation	operator: 29 operand: 33
27	Operation	operator: 31 operands: 32
28	Variable
29	Variable
30	ExprTuple	33
31	Literal
32	ExprTuple	34, 35
33	Variable
34	Variable
35	Variable