Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Forall, InSet, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = x_notequals_all_y, condition = NotInSet(x, Set(y_1_to_n))), InSet(n, Natural)))

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())

n \mapsto \left\{\forall_{x, y_{1}, y_{2}, \ldots, y_{n}~|~x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}}~\left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\right) \textrm{ if } n \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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