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, ExprTuple, 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 = ExprTuple(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(\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..\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: 2 body: 3
2	ExprTuple	32, 27
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	27, 11
10	Lambda	parameters: 31 body: 12
11	Operation	operator: 13 operand: 32
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	32
15	Operation	operator: 17 operands: 31
16	Operation	operator: 18 operands: 19
17	Literal
18	Literal
19	ExprTuple	20, 21
20	ExprRange	lambda_map: 22 start_index: 35 end_index: 36
21	Operation	operator: 23 operands: 24
22	Lambda	parameter: 40 body: 25
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Variable
28	Literal
29	ExprTuple	37, 32
30	Literal
31	ExprTuple	33
32	Variable
33	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
34	Lambda	parameter: 40 body: 37
35	Literal
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable