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 ExprTuple, 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 = ExprTuple(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())

\left(\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)\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	parameter: 29 body: 3
2	ExprTuple	29
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 15 operand: 10
7	Operation	operator: 42 operands: 9
8	ExprTuple	10
9	ExprTuple	11, 12
10	Lambda	parameter: 34 body: 13
11	Operation	operator: 15 operand: 18
12	Operation	operator: 15 operand: 19
13	Conditional	value: 25 condition: 17
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Operation	operator: 31 operands: 20
18	Lambda	parameter: 34 body: 21
19	Lambda	parameter: 34 body: 22
20	ExprTuple	34, 23
21	Conditional	value: 25 condition: 24
22	Conditional	value: 25 condition: 26
23	Operation	operator: 37 operands: 27
24	Operation	operator: 31 operands: 28
25	IndexedVar	variable: 29 index: 34
26	Operation	operator: 31 operands: 32
27	ExprTuple	39, 41
28	ExprTuple	34, 33
29	Variable
30	ExprTuple	34
31	Literal
32	ExprTuple	34, 35
33	Operation	operator: 37 operands: 36
34	Variable
35	Operation	operator: 37 operands: 38
36	ExprTuple	39, 44
37	Literal
38	ExprTuple	40, 41
39	Variable
40	Operation	operator: 42 operands: 43
41	Variable
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Literal