Expression of type Lambda

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

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.logic import Boolean, Forall, InSet
from proveit.logic.booleans.quantification import general_forall_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 = InSet(general_forall_Px, 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}~\left(\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{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: 15 operand: 7
4	Operation	operator: 11 operands: 6
5	ExprTuple	7
6	ExprTuple	24, 8
7	Lambda	parameter: 19 body: 10
8	Literal
9	ExprTuple	19
10	Operation	operator: 11 operands: 12
11	Literal
12	ExprTuple	13, 14
13	Operation	operator: 15 operand: 17
14	Literal
15	Literal
16	ExprTuple	17
17	Lambda	parameters: 20 body: 18
18	Operation	operator: 19 operands: 20
19	Variable
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