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, LessEq, Sum, one

# 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, b)), Sum(index_or_indices = sub_expr1, summand = fx, domain = Interval(Add(b, one), c)))), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), And(LessEq(a, b), LessEq(b, c)).with_total_ordering_style()))))

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} f\left(x\right)\right) + \left(\sum_{x = b + 1}^{c} f\left(x\right)\right)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  a \leq 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	56, 61, 58
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	11, 12, 13, 14
9	Operation	operator: 30 operand: 22
10	Operation	operator: 59 operands: 16
11	Operation	operator: 48 operands: 17
12	Operation	operator: 48 operands: 18
13	Operation	operator: 48 operands: 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	22
16	ExprTuple	23, 24
17	ExprTuple	56, 25
18	ExprTuple	61, 25
19	ExprTuple	58, 25
20	Literal
21	ExprTuple	26, 27
22	Lambda	parameter: 51 body: 28
23	Operation	operator: 30 operand: 35
24	Operation	operator: 30 operand: 36
25	Literal
26	Operation	operator: 32 operands: 53
27	Operation	operator: 32 operands: 33
28	Conditional	value: 42 condition: 34
29	ExprTuple	35
30	Literal
31	ExprTuple	36
32	Literal
33	ExprTuple	61, 58
34	Operation	operator: 48 operands: 37
35	Lambda	parameter: 51 body: 38
36	Lambda	parameter: 51 body: 39
37	ExprTuple	51, 40
38	Conditional	value: 42 condition: 41
39	Conditional	value: 42 condition: 43
40	Operation	operator: 54 operands: 44
41	Operation	operator: 48 operands: 45
42	Operation	operator: 46 operand: 51
43	Operation	operator: 48 operands: 49
44	ExprTuple	56, 58
45	ExprTuple	51, 50
46	Variable
47	ExprTuple	51
48	Literal
49	ExprTuple	51, 52
50	Operation	operator: 54 operands: 53
51	Variable
52	Operation	operator: 54 operands: 55
53	ExprTuple	56, 61
54	Literal
55	ExprTuple	57, 58
56	Variable
57	Operation	operator: 59 operands: 60
58	Variable
59	Literal
60	ExprTuple	61, 62
61	Variable
62	Literal