Expression of type Conditional

from the theory of proveit.logic.sets.enumeration

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, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Boolean, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = InSet(InSet(x, Set(y_1_to_n)), Boolean)), 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_{x, y_{1}, y_{2}, \ldots, y_{n}}~\left(\left(x \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \in \mathbb{B}\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: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	22, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	15, 19
9	Operation	operator: 13 operands: 10
10	ExprTuple	11, 12
11	Operation	operator: 13 operands: 14
12	Literal
13	Literal
14	ExprTuple	15, 16
15	Variable
16	Operation	operator: 17 operands: 18
17	Literal
18	ExprTuple	19
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 26 body: 23
21	Literal
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable