Expression of type ExprTuple

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, ExprTuple, IndexedVar, Lambda, 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}")
sub_expr2 = [x_1_to_n]
expr = ExprTuple(Lambda(sub_expr2, Conditional(Distinct(x_1_to_n), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), S), one, n), Equals(Len(operands = sub_expr2), 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(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 19 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 19
4	Operation	operator: 6 operands: 7
5	Literal
6	Literal
7	ExprTuple	8, 9
8	ExprRange	lambda_map: 10 start_index: 23 end_index: 24
9	Operation	operator: 11 operands: 12
10	Lambda	parameter: 28 body: 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	ExprTuple	25, 20
18	Literal
19	ExprTuple	21
20	Variable
21	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
22	Lambda	parameter: 28 body: 25
23	Literal
24	Variable
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable