Expression of type Conditional

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

# build up the expression from sub-expressions
sub_expr1 = [j]
sub_expr2 = Interval(c, d)
expr = Conditional(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))), And(InSet(c, Integer), InSet(d, 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\{\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) \textrm{ if } c \in \mathbb{Z} ,  d \in \mathbb{Z}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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