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, a, b, c, fx, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Integer, Interval, Less, LessEq, Sum, one, subtract

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda([a, b, c], Conditional(Equals(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(a, subtract(b, one))), Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(b, c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), Less(a, b), LessEq(b, 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(\left(a, b, c\right) \mapsto \left\{\left(\sum_{x = a}^{c} f\left(x\right)\right) = \left(\left(\sum_{x = a}^{b - 1} f\left(x\right)\right) + \left(\sum_{x = b}^{c} f\left(x\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a < b ,  b \leq c\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: 2 body: 3
2	ExprTuple	55, 60, 57
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12, 13, 14, 15, 16
10	Operation	operator: 31 operand: 25
11	Operation	operator: 58 operands: 18
12	Operation	operator: 47 operands: 19
13	Operation	operator: 47 operands: 20
14	Operation	operator: 47 operands: 21
15	Operation	operator: 22 operands: 23
16	Operation	operator: 24 operands: 54
17	ExprTuple	25
18	ExprTuple	26, 27
19	ExprTuple	55, 28
20	ExprTuple	60, 28
21	ExprTuple	57, 28
22	Literal
23	ExprTuple	55, 60
24	Literal
25	Lambda	parameter: 50 body: 29
26	Operation	operator: 31 operand: 34
27	Operation	operator: 31 operand: 35
28	Literal
29	Conditional	value: 41 condition: 33
30	ExprTuple	34
31	Literal
32	ExprTuple	35
33	Operation	operator: 47 operands: 36
34	Lambda	parameter: 50 body: 37
35	Lambda	parameter: 50 body: 38
36	ExprTuple	50, 39
37	Conditional	value: 41 condition: 40
38	Conditional	value: 41 condition: 42
39	Operation	operator: 53 operands: 43
40	Operation	operator: 47 operands: 44
41	Operation	operator: 45 operand: 50
42	Operation	operator: 47 operands: 48
43	ExprTuple	55, 57
44	ExprTuple	50, 49
45	Variable
46	ExprTuple	50
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 53 operands: 52
50	Variable
51	Operation	operator: 53 operands: 54
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	60, 57
55	Variable
56	Operation	operator: 58 operands: 59
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Variable
61	Operation	operator: 62 operand: 64
62	Literal
63	ExprTuple	64
64	Literal