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 Conditional, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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