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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(DecimalSequence(a_1_to_n), Natural), domain = Digits), InSet(n, NaturalPos))

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\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{N}^{\leq 9}}~\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{n}) \in \mathbb{N}\right) \textrm{ if } n \in \mathbb{N}^+\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: 3 operand: 6
2	Operation	operator: 25 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	24, 7
6	Lambda	parameters: 18 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 25 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprRange	lambda_map: 19 start_index: 23 end_index: 24
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 31 body: 21
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Operation	operator: 25 operands: 26
22	Lambda	parameter: 31 body: 27
23	Literal
24	Variable
25	Literal
26	ExprTuple	27, 28
27	IndexedVar	variable: 29 index: 31
28	Literal
29	Variable
30	ExprTuple	31
31	Variable