Expression of type Conditional

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, IndexedVar, Variable, a, b, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import DecimalSequence, Digits, NaturalPos, greater, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(InSet(DecimalSequence(a, b_1_to_n), NaturalPos), And(InSet(a, Digits), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Digits), one, n), greater(a, zero)))

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\{\texttt{\#}(a ~ b_{1}, b_{2}, \ldots, b_{n}) \in \mathbb{N}^+ \textrm{ if } a \in \mathbb{N}^{\leq 9}, \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) ,  a > 0\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 24 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 11 operands: 12
7	Literal
8	Operation	operator: 24 operands: 13
9	ExprRange	lambda_map: 14 start_index: 22 end_index: 23
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	20, 17
13	ExprTuple	20, 27
14	Lambda	parameter: 30 body: 18
15	Literal
16	ExprTuple	19, 20
17	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
18	Operation	operator: 24 operands: 25
19	Literal
20	Variable
21	Lambda	parameter: 30 body: 26
22	Literal
23	Variable
24	Literal
25	ExprTuple	26, 27
26	IndexedVar	variable: 28 index: 30
27	Literal
28	Variable
29	ExprTuple	30
30	Variable