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, Lambda, 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 = Lambda([S, N], 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(S, N\right) \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	31, 26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	26, 10
9	Lambda	parameters: 30 body: 11
10	Operation	operator: 12 operand: 31
11	Conditional	value: 14 condition: 15
12	Literal
13	ExprTuple	31
14	Operation	operator: 16 operands: 30
15	Operation	operator: 17 operands: 18
16	Literal
17	Literal
18	ExprTuple	19, 20
19	ExprRange	lambda_map: 21 start_index: 34 end_index: 35
20	Operation	operator: 22 operands: 23
21	Lambda	parameter: 39 body: 24
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Variable
27	Literal
28	ExprTuple	36, 31
29	Literal
30	ExprTuple	32
31	Variable
32	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
33	Lambda	parameter: 39 body: 36
34	Literal
35	Variable
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable