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, ExprRange, IndexedVar, N, S, Variable, n, x
from proveit.core_expr_types import Len, x_1_to_n
from proveit.logic import And, Distinct, Equals, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Distinct(x_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), S), one, n), Equals(Len(operands = [x_1_to_n]), 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\{\textrm{distinct}\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } \left(x_{1} \in S\right) ,  \left(x_{2} \in S\right) ,  \ldots ,  \left(x_{n} \in S\right) ,  |\left(x_{1}, x_{2}, \ldots, x_{n}\right)| = 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 operands: 17
2	Operation	operator: 4 operands: 5
3	Literal
4	Literal
5	ExprTuple	6, 7
6	ExprRange	lambda_map: 8 start_index: 21 end_index: 22
7	Operation	operator: 9 operands: 10
8	Lambda	parameter: 26 body: 11
9	Literal
10	ExprTuple	12, 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	Variable
14	Literal
15	ExprTuple	23, 18
16	Literal
17	ExprTuple	19
18	Variable
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