Expression of type Lambda

from the theory of proveit.logic.booleans.quantification.existence

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, P, n
from proveit.core_expr_types import P__y_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px, condition = P__y_1_to_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())

n \mapsto \left\{\forall_{P}~\left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{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: 32 body: 2
1	ExprTuple	32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operand: 8
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	32, 9
8	Lambda	parameter: 25 body: 11
9	Literal
10	ExprTuple	25
11	Operation	operator: 12 operand: 14
12	Literal
13	ExprTuple	14
14	Lambda	parameters: 20 body: 15
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 21
17	Operation	operator: 25 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	22
21	Lambda	parameters: 26 body: 23
22	ExprRange	lambda_map: 24 start_index: 31 end_index: 32
23	Operation	operator: 25 operands: 26
24	Lambda	parameter: 36 body: 27
25	Variable
26	ExprTuple	28
27	IndexedVar	variable: 29 index: 36
28	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
29	Variable
30	Lambda	parameter: 36 body: 33
31	Literal
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable