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, alpha, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, Sum, one

# build up the expression from sub-expressions
sub_expr1 = [k]
expr = ExprTuple(Lambda([a, b, c], Conditional(Forall(instance_param_or_params = [alpha], instance_expr = 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))))), 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\{\forall_{\alpha}~\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) \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	61, 66, 63
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 19 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12, 13
9	Lambda	parameter: 51 body: 15
10	Operation	operator: 53 operands: 16
11	Operation	operator: 53 operands: 17
12	Operation	operator: 53 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	51
15	Operation	operator: 21 operands: 22
16	ExprTuple	61, 23
17	ExprTuple	66, 23
18	ExprTuple	63, 23
19	Literal
20	ExprTuple	24, 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	Operation	operator: 28 operands: 58
25	Operation	operator: 28 operands: 29
26	Operation	operator: 37 operand: 32
27	Operation	operator: 64 operands: 31
28	Literal
29	ExprTuple	66, 63
30	ExprTuple	32
31	ExprTuple	33, 34
32	Lambda	parameter: 56 body: 35
33	Operation	operator: 37 operand: 40
34	Operation	operator: 37 operand: 41
35	Conditional	value: 47 condition: 39
36	ExprTuple	40
37	Literal
38	ExprTuple	41
39	Operation	operator: 53 operands: 42
40	Lambda	parameter: 56 body: 43
41	Lambda	parameter: 56 body: 44
42	ExprTuple	56, 45
43	Conditional	value: 47 condition: 46
44	Conditional	value: 47 condition: 48
45	Operation	operator: 59 operands: 49
46	Operation	operator: 53 operands: 50
47	IndexedVar	variable: 51 index: 56
48	Operation	operator: 53 operands: 54
49	ExprTuple	61, 63
50	ExprTuple	56, 55
51	Variable
52	ExprTuple	56
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 59 operands: 58
56	Variable
57	Operation	operator: 59 operands: 60
58	ExprTuple	61, 66
59	Literal
60	ExprTuple	62, 63
61	Variable
62	Operation	operator: 64 operands: 65
63	Variable
64	Literal
65	ExprTuple	66, 67
66	Variable
67	Literal