Expression of type Conditional

from the theory of proveit.logic.sets.cardinality

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, S
from proveit.core_expr_types import Len, x_1_to_n
from proveit.logic import Card, Distinct, Equals, Exists
from proveit.numbers import greater_eq

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
expr = Conditional(Exists(instance_param_or_params = sub_expr1, instance_expr = Distinct(x_1_to_n), domain = S, condition = Equals(Len(operands = sub_expr1), N)), greater_eq(Card(S), N))

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\{\exists_{x_{1}, x_{2}, \ldots, x_{n} \in S~|~|\left(x_{1}, x_{2}, \ldots, x_{n}\right)| = N}~\textrm{distinct}\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } |S| \geq 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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	24, 8
7	Lambda	parameters: 28 body: 9
8	Operation	operator: 10 operand: 29
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	29
12	Operation	operator: 14 operands: 28
13	Operation	operator: 15 operands: 16
14	Literal
15	Literal
16	ExprTuple	17, 18
17	ExprRange	lambda_map: 19 start_index: 32 end_index: 33
18	Operation	operator: 20 operands: 21
19	Lambda	parameter: 37 body: 22
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Variable
25	Literal
26	ExprTuple	34, 29
27	Literal
28	ExprTuple	30
29	Variable
30	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
31	Lambda	parameter: 37 body: 34
32	Literal
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable