Expression of type ExprTuple

from the theory of proveit.numbers.numerals.decimals

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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, c, d, k, m, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(d, sub_expr1), one, k)
sub_expr4 = Add(b_1_to_n)
expr = ExprTuple(Lambda([m, n, k], Conditional(Forall(instance_param_or_params = [sub_expr2, b_1_to_n, c, sub_expr3], instance_expr = Equals(DecimalSequence(sub_expr2, sub_expr4, sub_expr3), DecimalSequence(sub_expr2, c, sub_expr3)), domain = Digits, condition = Equals(sub_expr4, c)), And(InSet(m, Natural), InSet(n, Natural), InSet(k, Natural)))))

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(m, n, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}, c, d_{1}, d_{2}, \ldots, d_{k} \in \mathbb{N}^{\leq 9}~|~\left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) = c}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c ~ d_{1}, d_{2}, \ldots, d_{k})\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N} ,  k \in \mathbb{N}\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	48, 65, 50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 53 operands: 15
11	Operation	operator: 53 operands: 16
12	Operation	operator: 53 operands: 17
13	ExprTuple	40, 60, 46, 41
14	Conditional	value: 18 condition: 19
15	ExprTuple	48, 20
16	ExprTuple	65, 20
17	ExprTuple	50, 20
18	Operation	operator: 38 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28, 29, 30
24	Operation	operator: 32 operands: 31
25	Operation	operator: 32 operands: 33
26	ExprRange	lambda_map: 34 start_index: 64 end_index: 48
27	ExprRange	lambda_map: 35 start_index: 64 end_index: 65
28	Operation	operator: 53 operands: 36
29	ExprRange	lambda_map: 37 start_index: 64 end_index: 50
30	Operation	operator: 38 operands: 39
31	ExprTuple	40, 45, 41
32	Literal
33	ExprTuple	40, 46, 41
34	Lambda	parameter: 69 body: 42
35	Lambda	parameter: 69 body: 43
36	ExprTuple	46, 59
37	Lambda	parameter: 69 body: 44
38	Literal
39	ExprTuple	45, 46
40	ExprRange	lambda_map: 47 start_index: 64 end_index: 48
41	ExprRange	lambda_map: 49 start_index: 64 end_index: 50
42	Operation	operator: 53 operands: 51
43	Operation	operator: 53 operands: 52
44	Operation	operator: 53 operands: 54
45	Operation	operator: 55 operands: 56
46	Variable
47	Lambda	parameter: 69 body: 57
48	Variable
49	Lambda	parameter: 69 body: 58
50	Variable
51	ExprTuple	57, 59
52	ExprTuple	66, 59
53	Literal
54	ExprTuple	58, 59
55	Literal
56	ExprTuple	60
57	IndexedVar	variable: 61 index: 69
58	IndexedVar	variable: 62 index: 69
59	Literal
60	ExprRange	lambda_map: 63 start_index: 64 end_index: 65
61	Variable
62	Variable
63	Lambda	parameter: 69 body: 66
64	Literal
65	Variable
66	IndexedVar	variable: 67 index: 69
67	Variable
68	ExprTuple	69
69	Variable