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, k, m
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Less, Natural, nine, one, zero

# 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)
expr = ExprTuple(Lambda([m, k], Conditional(Forall(instance_param_or_params = [sub_expr2, b], instance_expr = Equals(Add(DecimalSequence(sub_expr2, b, ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(sub_expr2, Add(b, one), ExprRange(sub_expr1, zero, one, k))), domain = Digits, condition = Less(b, nine)), And(InSet(m, 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, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b \in \mathbb{N}^{\leq 9}~|~b < 9}~\left(\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b ~ 9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b + 1\right) ~ 0, 0, ..\left(k - 3\right) \times.., 0)\right) \textrm{ if } m \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	51, 54
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 43 operands: 14
11	Operation	operator: 43 operands: 15
12	ExprTuple	45, 47
13	Conditional	value: 16 condition: 17
14	ExprTuple	51, 18
15	ExprTuple	54, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26, 27
23	Operation	operator: 40 operands: 28
24	Operation	operator: 38 operands: 29
25	ExprRange	lambda_map: 30 start_index: 53 end_index: 51
26	Operation	operator: 43 operands: 31
27	Operation	operator: 32 operands: 33
28	ExprTuple	34, 53
29	ExprTuple	45, 35, 36
30	Lambda	parameter: 59 body: 37
31	ExprTuple	47, 49
32	Literal
33	ExprTuple	47, 56
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operands: 41
36	ExprRange	lambda_map: 42 start_index: 53 end_index: 54
37	Operation	operator: 43 operands: 44
38	Literal
39	ExprTuple	45, 47, 46
40	Literal
41	ExprTuple	47, 53
42	Lambda	parameter: 59 body: 48
43	Literal
44	ExprTuple	55, 49
45	ExprRange	lambda_map: 50 start_index: 53 end_index: 51
46	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
47	Variable
48	Literal
49	Literal
50	Lambda	parameter: 59 body: 55
51	Variable
52	Lambda	parameter: 59 body: 56
53	Literal
54	Variable
55	IndexedVar	variable: 57 index: 59
56	Literal
57	Variable
58	ExprTuple	59
59	Variable