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, Q, n
from proveit.logic import Boolean, Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = InSet(general_exists_Py_st_Qy, Boolean)), 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, Q}~\left(\left[\exists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\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: 28 body: 2
1	ExprTuple	28
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 12 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	28, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	22, 23
11	Operation	operator: 12 operands: 13
12	Literal
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 18
15	Literal
16	Literal
17	ExprTuple	18
18	Lambda	parameters: 24 body: 19
19	Conditional	value: 20 condition: 21
20	Operation	operator: 22 operands: 24
21	Operation	operator: 23 operands: 24
22	Variable
23	Variable
24	ExprTuple	25
25	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
26	Lambda	parameter: 32 body: 29
27	Literal
28	Variable
29	IndexedVar	variable: 30 index: 32
30	Variable
31	ExprTuple	32
32	Variable