Expression of type Forall

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 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 = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [P], instance_expr = InSet(general_forall_Px, Boolean)), domain = 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())

\forall_{n \in \mathbb{N}^+}~\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)\right]

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 17 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 26 body: 4
3	ExprTuple	26
4	Conditional	value: 5 condition: 6
5	Operation	operator: 17 operand: 9
6	Operation	operator: 13 operands: 8
7	ExprTuple	9
8	ExprTuple	26, 10
9	Lambda	parameter: 21 body: 12
10	Literal
11	ExprTuple	21
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operand: 19
16	Literal
17	Literal
18	ExprTuple	19
19	Lambda	parameters: 22 body: 20
20	Operation	operator: 21 operands: 22
21	Variable
22	ExprTuple	23
23	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
24	Lambda	parameter: 30 body: 27
25	Literal
26	Variable
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable