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, a, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos, greater, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b_1_to_n], instance_expr = InSet(DecimalSequence(a, b_1_to_n), NaturalPos), domain = Digits, condition = greater(a, zero)), InSet(n, 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\{\forall_{a, b_{1}, b_{2}, \ldots, b_{n} \in \mathbb{N}^{\leq 9}~|~a > 0}~\left(\texttt{\#}(a ~ b_{1}, b_{2}, \ldots, b_{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: 32 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	31, 7
6	Lambda	parameters: 20 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 32 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17, 18
14	Operation	operator: 19 operands: 20
15	Literal
16	Operation	operator: 32 operands: 21
17	ExprRange	lambda_map: 22 start_index: 30 end_index: 31
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	28, 25
21	ExprTuple	28, 35
22	Lambda	parameter: 38 body: 26
23	Literal
24	ExprTuple	27, 28
25	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
26	Operation	operator: 32 operands: 33
27	Literal
28	Variable
29	Lambda	parameter: 38 body: 34
30	Literal
31	Variable
32	Literal
33	ExprTuple	34, 35
34	IndexedVar	variable: 36 index: 38
35	Literal
36	Variable
37	ExprTuple	38
38	Variable