Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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