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 Equals, 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 = Equals(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y)), 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}}~\left(\left(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\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)\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	33, 26
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	33, 21
19	Literal
20	ExprTuple	22
21	Operation	operator: 23 operands: 24
22	ExprRange	lambda_map: 25 start_index: 29 end_index: 30
23	Literal
24	ExprTuple	26
25	Lambda	parameter: 37 body: 27
26	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
27	Operation	operator: 31 operands: 32
28	Lambda	parameter: 37 body: 34
29	Literal
30	Variable
31	Literal
32	ExprTuple	33, 34
33	Variable
34	IndexedVar	variable: 35 index: 37
35	Variable
36	ExprTuple	37
37	Variable