Expression of type Conditional

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

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = InSet(general_forall_Px_if_Qx, 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())

\left\{\forall_{P, Q}~\left(\left[\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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