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, n
from proveit.core_expr_types import Len, x_1_to_n
from proveit.logic import Card, Distinct, Equals, Exists, Forall, InSet
from proveit.numbers import NaturalPos, greater_eq

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [S, N], instance_expr = Exists(instance_param_or_params = sub_expr1, instance_expr = Distinct(x_1_to_n), domain = S, condition = Equals(Len(operands = sub_expr1), N)), condition = greater_eq(Card(S), N)), InSet(n, NaturalPos))))

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(n \mapsto \left\{\forall_{S, N~|~|S| \geq N}~\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)\right] \textrm{ if } n \in \mathbb{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	parameter: 45 body: 3
2	ExprTuple	45
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 37 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	45, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 36
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	36, 20
19	Lambda	parameters: 40 body: 21
20	Operation	operator: 22 operand: 41
21	Conditional	value: 24 condition: 25
22	Literal
23	ExprTuple	41
24	Operation	operator: 26 operands: 40
25	Operation	operator: 27 operands: 28
26	Literal
27	Literal
28	ExprTuple	29, 30
29	ExprRange	lambda_map: 31 start_index: 44 end_index: 45
30	Operation	operator: 32 operands: 33
31	Lambda	parameter: 49 body: 34
32	Literal
33	ExprTuple	35, 36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	Variable
37	Literal
38	ExprTuple	46, 41
39	Literal
40	ExprTuple	42
41	Variable
42	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
43	Lambda	parameter: 49 body: 46
44	Literal
45	Variable
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable