Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([c, d], 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(c, d\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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