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, b, c, d, k, m, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, DecimalSequence, Digits, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = IndexedVar(d, sub_expr1)
sub_expr4 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr5 = ExprRange(sub_expr1, sub_expr3, one, k)
sub_expr6 = Add(b_1_to_n)
expr = ExprTuple(Lambda([sub_expr4, b_1_to_n, c, sub_expr5], Conditional(Equals(DecimalSequence(sub_expr4, sub_expr6, sub_expr5), DecimalSequence(sub_expr4, c, sub_expr5)), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Digits), one, n), InSet(c, Digits), ExprRange(sub_expr1, InSet(sub_expr3, Digits), one, k), Equals(sub_expr6, 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_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}, c, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \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}) \textrm{ if } \left(a_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(a_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(a_{m} \in \mathbb{N}^{\leq 9}\right), \left(b_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(b_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(b_{n} \in \mathbb{N}^{\leq 9}\right) ,  c \in \mathbb{N}^{\leq 9}, \left(d_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(d_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{N}^{\leq 9}\right) ,  \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) = 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	25, 45, 31, 26
3	Conditional	value: 4 condition: 5
4	Operation	operator: 23 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14, 15
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	ExprRange	lambda_map: 19 start_index: 49 end_index: 33
12	ExprRange	lambda_map: 20 start_index: 49 end_index: 50
13	Operation	operator: 38 operands: 21
14	ExprRange	lambda_map: 22 start_index: 49 end_index: 35
15	Operation	operator: 23 operands: 24
16	ExprTuple	25, 30, 26
17	Literal
18	ExprTuple	25, 31, 26
19	Lambda	parameter: 54 body: 27
20	Lambda	parameter: 54 body: 28
21	ExprTuple	31, 44
22	Lambda	parameter: 54 body: 29
23	Literal
24	ExprTuple	30, 31
25	ExprRange	lambda_map: 32 start_index: 49 end_index: 33
26	ExprRange	lambda_map: 34 start_index: 49 end_index: 35
27	Operation	operator: 38 operands: 36
28	Operation	operator: 38 operands: 37
29	Operation	operator: 38 operands: 39
30	Operation	operator: 40 operands: 41
31	Variable
32	Lambda	parameter: 54 body: 42
33	Variable
34	Lambda	parameter: 54 body: 43
35	Variable
36	ExprTuple	42, 44
37	ExprTuple	51, 44
38	Literal
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	45
42	IndexedVar	variable: 46 index: 54
43	IndexedVar	variable: 47 index: 54
44	Literal
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	Variable
47	Variable
48	Lambda	parameter: 54 body: 51
49	Literal
50	Variable
51	IndexedVar	variable: 52 index: 54
52	Variable
53	ExprTuple	54
54	Variable