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 Lambda, a, alpha, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Lambda(alpha, Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c)))))

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())

\alpha \mapsto \left(\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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