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, fi, i, j, k, 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 = [i]
sub_expr2 = Interval(j, k)
expr = Lambda([j, k], Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = Mult(x, fi), domain = sub_expr2), Mult(x, Sum(index_or_indices = sub_expr1, summand = fi, domain = sub_expr2))), And(InSet(j, Integer), InSet(k, 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(j, k\right) \mapsto \left\{\left(\sum_{i = j}^{k} \left(x \cdot f\left(i\right)\right)\right) = \left(x \cdot \left(\sum_{i = j}^{k} f\left(i\right)\right)\right) \textrm{ if } j \in \mathbb{Z} ,  k \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: 37 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: 24 operands: 13
10	Operation	operator: 32 operands: 14
11	Operation	operator: 32 operands: 15
12	ExprTuple	16
13	ExprTuple	27, 17
14	ExprTuple	38, 18
15	ExprTuple	39, 18
16	Lambda	parameter: 34 body: 19
17	Operation	operator: 20 operand: 23
18	Literal
19	Conditional	value: 22 condition: 29
20	Literal
21	ExprTuple	23
22	Operation	operator: 24 operands: 25
23	Lambda	parameter: 34 body: 26
24	Literal
25	ExprTuple	27, 28
26	Conditional	value: 28 condition: 29
27	Variable
28	Operation	operator: 30 operand: 34
29	Operation	operator: 32 operands: 33
30	Variable
31	ExprTuple	34
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable