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.logic import And, Equals, InSet
from proveit.numbers import 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(c, sub_expr1)
sub_expr4 = IndexedVar(d, sub_expr1)
sub_expr5 = ExprRange(sub_expr1, b, one, n)
sub_expr6 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr7 = ExprRange(sub_expr1, sub_expr3, one, n)
sub_expr8 = ExprRange(sub_expr1, sub_expr4, one, k)
expr = ExprTuple(Lambda([sub_expr6, b, sub_expr7, sub_expr8], Conditional(Equals(DecimalSequence(sub_expr6, sub_expr5, sub_expr8), DecimalSequence(sub_expr6, sub_expr7, sub_expr8)), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), InSet(b, Digits), ExprRange(sub_expr1, InSet(sub_expr3, Digits), one, n), ExprRange(sub_expr1, InSet(sub_expr4, Digits), one, k), Equals([sub_expr5], [sub_expr7])))))

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, c_{1}, c_{2}, \ldots, c_{n}, d_{1}, d_{2}, \ldots, d_{k}\right) \mapsto \left\{\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b, b, ..\left(n - 3\right) \times.., b ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c_{1}, c_{2}, \ldots, c_{n} ~ 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) ,  b \in \mathbb{N}^{\leq 9}, \left(c_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(c_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(c_{n} \in \mathbb{N}^{\leq 9}\right), \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, b, ..\left(n - 3\right) \times.., b\right) = \left(c_{1}, c_{2}, \ldots, c_{n}\right)\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, 51, 41, 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: 47 end_index: 33
12	Operation	operator: 38 operands: 20
13	ExprRange	lambda_map: 21 start_index: 47 end_index: 48
14	ExprRange	lambda_map: 22 start_index: 47 end_index: 35
15	Operation	operator: 23 operands: 24
16	ExprTuple	25, 40, 26
17	Literal
18	ExprTuple	25, 41, 26
19	Lambda	parameter: 55 body: 27
20	ExprTuple	51, 44
21	Lambda	parameter: 55 body: 28
22	Lambda	parameter: 55 body: 29
23	Literal
24	ExprTuple	30, 31
25	ExprRange	lambda_map: 32 start_index: 47 end_index: 33
26	ExprRange	lambda_map: 34 start_index: 47 end_index: 35
27	Operation	operator: 38 operands: 36
28	Operation	operator: 38 operands: 37
29	Operation	operator: 38 operands: 39
30	ExprTuple	40
31	ExprTuple	41
32	Lambda	parameter: 55 body: 42
33	Variable
34	Lambda	parameter: 55 body: 43
35	Variable
36	ExprTuple	42, 44
37	ExprTuple	52, 44
38	Literal
39	ExprTuple	43, 44
40	ExprRange	lambda_map: 45 start_index: 47 end_index: 48
41	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
42	IndexedVar	variable: 49 index: 55
43	IndexedVar	variable: 50 index: 55
44	Literal
45	Lambda	parameter: 55 body: 51
46	Lambda	parameter: 55 body: 52
47	Literal
48	Variable
49	Variable
50	Variable
51	Variable
52	IndexedVar	variable: 53 index: 55
53	Variable
54	ExprTuple	55
55	Variable