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 Boolean, Forall, InSet, Set
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 = InSet(InSet(x, Set(y_1_to_n)), Boolean)), 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 \in \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \in \mathbb{B}\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: 24 body: 2
1	ExprTuple	24
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 15 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	24, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	17, 21
11	Operation	operator: 15 operands: 12
12	ExprTuple	13, 14
13	Operation	operator: 15 operands: 16
14	Literal
15	Literal
16	ExprTuple	17, 18
17	Variable
18	Operation	operator: 19 operands: 20
19	Literal
20	ExprTuple	21
21	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
22	Lambda	parameter: 28 body: 25
23	Literal
24	Variable
25	IndexedVar	variable: 26 index: 28
26	Variable
27	ExprTuple	28
28	Variable